I don't really see anything wrong with paying by Paypal? It's basically a bank transfer.
There are different laws in different states. I know you said you aren't going to buy this horse, but it may have been weird legally for you if you'd bought in another state. You can find blank horse purchasing contracts online.
We had to return a horse once (a "beginner-safe bombproof" horse who was spooky, bucked, and kicked; even found out later that we were the third purchase to return him). The contract worked well for us, because we had everything spelled out, even who was responsible for transportation costs. The owner lived far away from us. My husband drove him all the way down there and she gave him an envelope with cash. He didn't count it but found out later she had shorted us.
We've gone through a lot looking for a horse and ended up at the same place you are (sticking with lessons). What I've learned, sometimes the hard way, is that there are a lot of people out there who will lie about the horse they are trying to sell. Our next purchase will involve many pre-purchase rides and a trial period in the new setting.