In Florida, it is inherent risks you are waiving, and if you sign a waiver saying you have been apprised of the risks, under law you cannot sue for the "inherent risks" of equine activity. However, if you can show negligence caused injuries, that is a different case. I would imagine that is the case in most states.
Waivers for inherent risks are one thing, but waivers for negligence, gross negligence or even higher standards are a different matter. For instance, if a trainer knowingly puts a little kid who has never ridden before on a hot, green horse they know to be dangerous and that horse freaks and permanently injures the child, that is not an inherent risk - it was entirely avoidable and thus falls under a different standard. If I read a waiver that includes language indemnifying a provider (equestrian, doctor or otherwise) for negligence or other similar standards, I think long and hard before I sign it and sometimes strike through the objectionable language and initial (which is perfectly legal) before signing. It's not because I want to sue anyone, it's simply that someone who feels the need to protect themselves from such actions might not take the care they should.
As for waivers, you absolutely can sign away your rights to sue (actually, you can sign away your rights to just about anything, including your constitutional rights) and such contracts, if executed properly can be binding, which is why it can be really important to read medical intake papers, auto purchase papers and other forms fully before you sign them so you know if they include waivers (some of them are pretty sneaky) and make an informed choice whether or not to sign them.