Depends on the individual horse. I can tell you right now my TB mare will not be called "old" until she is physically incapable of walking another step! My Paso Fino is my "old guy" at 23, though he looks like a 3-yr old IMO. He has moonblindness in one eye and is the gentle, grumpy grandpa of the farm, so he's my senior. I don't think 17 is old though.....but again, it all depends on the horse.
My Lacey girl is 25, 26 in the spring, and she certainly doesn't look or act her age. I suppose, if you looked hard and had a picture of her not moving, you could probably see the age. But if you saw a picture of her moving or just saw her irl, you'd have no idea.
She does get stiff if I only work with her once a week so I try to get her moving 3-4 times a week and that seems to keep her younger feeling. For instance, on Monday we went for a ride that ended up being a couple miles (maybe 3-4 round trip) long over rather steep terrain and she was sweaty but not too pooped when we got home and the next day she was raring to go again!
My old gelding is in his mid 30's, I got him when I was 12, almost 13 years ago, he was sold to us as 15, but the vet said he was 20-25, which would put him at 33-38, and besides missing all but 4 of his bottom molars he is in great shape, with his attitude I have trouble calling him old, he chases my 13 year old OTTB mare and my 20ish year old appy gelding around the field biting their buts and kicking at them when they get out of line lol
Here is a pic of him that I took in the beginning of july
I think the comment that all horses age differently is very valid. A racehorse that was raced heavily as a 2yo compared to horse that wasn't broken in until he was 4 will have very different levels of degeneration.
A horse is very unlikely to drop dead at 18 through natural causes though there level of joint degeneration/ arthritis etc etc will affect how much work they can do
I used to work at a therapeutic riding school for disabled kids, we specialized in old horses as they would not react to the kids. Two years ago we retired a 34 year old horse who is still alive and well. Of course he had the best diet and has always been well care for since becoming part of the program many years ago.
He was also the most dominant in the pasture at 34 before he retired.