Well my mare isn't old by any means, but she is the oldest horse I have owned at 12 years of age.
I get asked at least twice a month how old she is because people assume she's much, much younger based on her behaviour!
She is just so active and alert, she is often referred to as the "busiest" horse at our stables.
Honestly I can't picture her settling down any time soon. I bet that a few years from now when she is 17-19 she will still be busy, busy Bling!
I think each horse and rider is different. I wouldn't hesitate about buying an older horse similar to my mare - because she is amazing to me. On the other hand though, I may be hard pressed to buy an older horse with a 'quieter' temperament since they are likely to get slower as they age. I like my horses to move forward. I don't really have the patience for horses who have a lot of resistance. Horses that don't go forward when you kick them 100000 times frustrates me to no end, and I ain't got no time for that!
These types of horses are the reason I could never be a trainer...
Some people of course value a nice quiet horse and so will often look for older horses because of this. Not me, but that's just my preference. I know my boyfriend, a true beginner, would be very nervous on a horse like my mare and would probably prefer an older horse with a little less pep.
I think it really depends on whether the horse and rider mesh in personalities and values. But remember that older horses come in different personalities too! Not all of them are old at heart.