Honestly it all depends on the horse and the situation. Some horses can handle being outside, some flourish outside, and others can't handle it at all. It also depends on what sort of pasture and what protection your horse will have from the elements.
Things to think about in regards to the pasture:
How many acres will the horse be on? Will it have a multiple shelters to choose from? One shed isn't always sufficient; if the horse is low in the pecking order it may be kept out by the other horses. Will the horse be fed grain? How about hay? Will the horse be brought in to eat or will it be fed in the pasture? If it is fed in the pasture will the hay/grain be widely dispersed so that even low-ranking horses can eat? Is the pasture in good shape? Has it been cleared of all debris and toxic plants? Does the pasture have good drainage and/or an elevated area? In other words, will the pasture turn into a complete mud pit when it rains?
Things to think about in regards to the horse:
Does the horse have a history of illness? If so, what? How was the horse kept at its previous home? If it was stabled a lot then it may not be best to keep it out. Will you be buying the horse any sort of fly or rain protection? Is the horse dominant or submissive? Will the horse have shoes? Will the other horses in the pasture have shoes? If a horse is kicked by another horse in shoes then it can cause a lot more damage. Are there any particularly aggressive horses in the pasture? Will the horse come to you in a pasture (trust me, if your horse is in a 60 acre pasture like mine then this is important!)? Does the horse have a history of being buddy sour? If the horse does get injured or ill where will it stay? Will you be able to keep it in a stall or will you be forced to keep it outside?
Things to ask about yourself:
How often will you be out to work with the horse? Will you be able to check it often for injuries or illness? Will you be able to recognize and treat any injuries or illnesses? What will you do if the horse DOES get ill or injured? What will you do if you can't afford to treat it? Will you abandon the horse? Go into debt? Let it die slowly? Euthanize it?
As you can see, there's a lot to consider. I personally prefer to leave a horse out to pasture if at all possible. However, I keep my horses in a place where they have access to a 60 acre pasture but are still able to be brought in to a stall in inclement weather and unusual circumstances. Horses are designed to live outside, not cooped up in a 12 x 12 box. If at all possible I believe they should be allowed to be horses.
However, that doesn't mean that you should consider pasture board as a cost-saving method. Sure, it's cheaper and that's always nice but that should not be the deciding factor. You should do what's best for your horse, not your wallet. If you can't keep both your wallet AND your horse happy and healthy then you may want to consider different options. For instance, leasing may be a good choice. A half lease is usually quite reasonable and if the horse does come down with an illness or injury you aren't left to pay for it entirely on your own (unless it's your fault, of course).
My horses, and most I've known, thrive when allowed to be horses. If your horse can be kept outside then that's wonderful. However, pasture board should only ever be considered if the facilities are appropriate and the horse can handle it. To determine whether or not pasture board is a good option for your horse you may have to do a bit of research and consider speaking to a knowledgeable horse person or veterinarian.
Good luck!