My trainer lady has a 34 year old horse that is still being ridden pretty often and he's totally fine with it. Her young daughter rides him and since she's young she doesn't ride him hard, no major hill climbing/cantering etc, and they're great together.
Like Jubilee said don't assume this horse is dead broke or not spooky just because of his age. I have a 24 year old mare that is a major challenge and that I wouldn't feel comfortable letting anyone who's not an expierenced rider on, regardless of their age. And even though she's older she can be ridden for hours with no problem at all. If she were 27 or so I'd be more concerned about riding her too long/often, but she's not. =)
I'd say go for it. Just be sure to get a vet check and make sure the horse is the right personality. 20 isn't very old at all, he could still have ten or more good years of riding and teaching left in him.