There's really no way around it.
Even if everyone in the club agrees that any injuries are their own problem, their health insurance company might not agree. They can sue the pants off you, without the permission of the injured person, and they will. They're not going to put up megabucks for a big injury if they can get reimbursed by someone else.
That someone else could be the landowner involved or the club or YOU.
Even if they don't ultimately win the case, you'll have to have a lawyer to defend you, and you're likely to lose on top of it.
Some states have horse liability laws, where no one's liable for someone else's horse related injuries if that person chose to participate. However, if you ever ride anywhere public, that wouldn't cover you - for example, if you rode down the street and your horse kicked someone, you'd be liable. That person wasn't participating in your horse-related activity, so they can sue you and win.
Club insurance policies are available quite cheaply. My numbers are out of date, of course, but 10 years ago when I ran a 4H club it was like $100 +$2.50 per member for our 4H club. That's less than $2 a week. Well worth it.
So before you decide NOT to have this very necessary protection, find out how much it's going to cost, and weigh that against what you could lose if you're sued.