First of all, congratulations on the impending arrival !!! Your mare can be allowed to foal in either place- but there are several things you may want to take into consideration when making your choice as to where she does. First, size matters. Is your mare's stall a foaling stall? Foaling stalls are normally at least 12x12 feet wide, and many of them are 14x14 or 16x16. The stall must be wide enough for BOTH mare and foal to lie down comfortably, and there must also be room enough in there for you and possibly the vet to work. If the stall is NOT wide enough, the mare may have to foal outside. Next on the list is cleanliness. Regardless of where your mare gives birth, it is IMPERATIVE for BOTH her health and the foal's health that the enviornment be scrupulously clean and sanitary.
Both the stall and the paddock need to be clean and free of obvious hazards, such as nails in walls or fencing. In addition, both places need to be free of manure and, in the case of the stall, exessive dirt, cobwebs, and dust. Mares who are foaling need to be bedded on straw, NOT shavings or sawdust, and the bedding needs to be very deep ( at least 6-8 inches) for the protection of the foal when it starts to scramble around prior to standing up for the first time. The other reason for using straw is that shavings will cling to the foal's wet coat, and they can cause an infection if they get into the navel stump and travel into the foal's system. The navel is what is left after the umbilical cord breaks, and it must be cleaned and treated immediately, because it is an open wound and a potential source of serious infections in the baby.
Straw is also easier to clean up and replace ( and you will be doing quite a bit of that right after the foal is born, because there is always a certain amount of bleeding associated with the birth process, and it tends to make a mess) and is less costly than shavings. Now, if you decide to let your mare foal outside, you will want to make sure of a couple more things. One of these concerns your fencing- if you have a post and board, or a post and rail fence, or a high-tension wire fence, then you will need to make sure that you run some fine wire mesh fencing around the inside of the paddock.
The reason for this is to prevent the baby from rolling under the fence and either getting trapped under there ( which will result in panic and serious injuries to both mare and foal) or possibly rolling out to the other side of the fence and getting loose. Wire mesh fencing material is available at most farm and hardware stores, and it can also be ordered online from several different companies. The product is easy to install, and it is well worth it if you want to protect your new foal.
The other issue with foaling outside is the type of footing the mare will be standing and foaling on- if the paddock is at all muddy, or if it has lots of manure on the ground, or if you don't have anything like a run-in shed where your mare can get out of the weather, then you need to keep her inside at night until she foals. Most mares foal at night or in the early ( pre-dawn) hours of the morning- this is a carry over from when horses were wild and lived in herds. There was less danger from predators at night ( most were not as active) and it was safer for the new baby . If your paddock has good grass and is not muddy, then the mare can foal outside as long as the weather will allow- but she should NOT be exposed to high heat, severe cold, or rain mixed with cold weather. Some final notes on this topic: Make sure that you tell your vet that your mare is close to foaling ( likely, he or she already is aware of this, but it is good to remind the vet anyway) and that you have your foaling kit ready. I would also recommend that you read as much as you can about foaling and foals- and there are several really good books on the subject available.
Foaling kits are easy to make. Basically, you need lots of old towels, a couple of clean sponges, the makings for a bran mash for the mare ( her first meal after the baby is born should be a bran mash) 10% ( strong ) tincture of iodine, a shot glass ( for treating the foal's naval after birth) a bucket or another container for storing the afterbirth once the mare passes it, standard stall cleaning equipment , and you may want to ask your vet about having some Banamine on hand to give your mare in case she has after pains that are severe.
Make sure that you save the afterbirth once the mare passes it- and initially, you will want to tie it up so that she can't step on it when she walks around. The vet will want to come and see your mare right after she foals, and will need to see the afterbirth to make sure the mare has passed it all. He or she will also examine the baby to make sure it is healthy and nursing normally, and will give the baby a tetanus shot. One other thing that should be part of your foaling kit- you need to make sure that you have a tail wrap or sheath for the mare. This will keep the mare's tail clean ( she won't get blood on it) and out of the way, and will help reduce the risk of infection to both her and the baby. The tail wrap should be applied about 8 to 12 hours before the mare foals, and left on until after she passes the afterbirth. Once it is removed, make sure that you wash it !! I used to work on a breeding farm, and I have attended the births of several foals, which is why I know as much as I do about this subject. I also have a mare who I will be breeding this month for a foal next spring- and she is also a maiden mare, just like yours. I want to wish you good luck, and I hope this helps you with your decision.
PS:After reading this response again, I realized that I forgot to mention that no matter where your mare gives birth, you will need to have both hot and cold water handy. Hot water will be needed to make bran mash, and you will want to have some tepid or warm water available after the mare foals so that you can wash her back legs and external genitalia. This is important to do, because it is late spring now and the bugs are starting to really come out- and there is nothing that flies and stinging insects like better than dried blood and birth fluids. They will drive your mare crazy- so she needs to be clean before she and the baby go outside for the first time together. Speaking of turnout, your mare and the new foal need to be turned out ALONE for the first 10 to 15 days after the baby is born. Do NOT try to integrate the pair into another field where there are other mares and foals before this, as the baby will not be strong enough to avoid injuries when playing. And, please, NEVER put your mare and her baby in a field where there are older adult horses ( or even yearlings and 2 year olds) who do not have foals or are geldings. This type of situation is extremely dangerous for both mother and baby- because the older horses will often attack and may seriously injure or kill the foal. (We had more than one near miss on the breeding farm where I used to work, that came about from just this type of situation- and it isn't pretty to have to treat the injuries that come from a panicked foal who has nearly been driven into the ground by other horses. Don't try to rely on the mare to protect her foal- she is only one horse, and she can be outnumbered quickly.)
One other thing I forgot to mention earlier- It is extremely important that your new foal get its first meal within 12 hours of birth. This is because the first milk, which is called colostrum, contains antibodies that will protect the foal from disease until its immune system is developed enough to do the job. The foal's system is only able to absorb these antibodies for about 12 hours or so, and then the chemistry of the gut changes and this is no longer as easy. That is why it is so critical that the baby nurse immediately. If your new foal seems to be uninterested in nursing, or appears to be unable to nurse normally- you need to get your vet to look at it right away, as the baby's life could be threatened by this. Nursing has benefits for the mare as well- it is one of the things that helps her shed or pass the placenta, and it helps relieve after pains that sometimes happen. It's important for the mare's health that she passes the placenta normally and in one complete piece- a mare that retains even part of it will develop serious infections and can also develop founder ( the same terrible disease that killed the racehorse, Barbaro, last January) which could result in death. I do not say this to scare you- but you need to be aware of the potential complications that can result from foaling, even in a maiden mare. Again, good luck- and congratulations !!!