Well, I am going to play devil's advocate and say stay because if he rides he is just going to get more sick, fall off his horse, have it stolen too and then what? So, I say beg the inn keeper for mercy or when he's not looking bang him on the head with a frying pan, take the horse anyway. Hmmm... perhaps I should tell that to my therapist?
I actually think he should ASK for help, like Rand and Mat did with Basel Gil (that happens so early in the books that I can't see calling it a spoiler ). You never know, the innkeeper could be a good man. And I wouldn't want to be without my sword.