am I responsible

Just remember, even if you have a waiver, that can go to crap pretty easily. It's always good to have them, but everything I've ever heard they don't amount to much. Equally important have the Inherent Risk Law posted at your barn.

I used to let people ride my horse, but no more. Not in this world. Just not worth the risk.

^^ Good idea ;)
I'd hate for you to be sued for having not done something so simple! And it can be simple--" I agree to hold [your farm name] harmless to any harm that might be done against myself while on your property..blah blah blah..{sign here} "
And hang the "Equine Sign" in your barn!
We always have someone sign a release if they are going to be doing any horse activity at our place, along with the "Equine Sign" hanging in our barn..

I think it's very important for everyone to realize that, as has been stated, a waiver does not carry any guarantees. Depending on the degree of injury, and how it happened, a court can still decide in favor of the plaintiff. Often, it doesn't even have to do with anything personal, but if you're in the US and get seriously injured riding someone elses horse, who's going to pay for your medical coverage? If it were me, I'd personally feel guilty if someone got hurt riding my horse, regardless of how it happened, and couldn't pay the medical bills.

I'm not sure how insurance works in the US, but here in Canada the horses are tacked onto the house insurance. Did you know if your horse gets loose and hit by a car, YOU are responsible for the damages caused to the person driving and his/her car? It's a lot of little things horse owners don't realize.

Insurance really is the best way to go. Insurance not only reimburses the cost of the horse if something happens in an accident, but also covers the cost of you being sued. Waivers are still a good thing to help, but they DON'T protect you, so don't fool yourself into believeing a piece of paper will get you out of hot water even if the resulting accident was 100% the fault of the rider. It was your property and your horse, so just be prepared.

I am in Florida and at our barn we sign releases and have the Florida horse inherent danger law signs posted all over.

We do at our barn too. They are posted at most of the major facilities but it sure doesn't keep people from suing. Even if they come of their own horse!