Although the vast majority of dogs I see for training are either puppies or young adults, that doesn’t mean older dogs are out of luck! Older dogs can be trained, there are just a few things to keep in mind:
As long as the brain is working as it should, a dog is never too old to learn. In fact, training and brain games are great ways to provide enrichment for an older dog whose body isn’t as capable as it once was. Just because the body is stiff and slow doesn’t mean he can’t exercise his brain. Something like Match to Sample is a great skill to work on and it makes an impressive party trick!
Age does inhibit a dog physically, just like it does humans. For example, your 10 year dog is probably too old to learn to Beg/Sit Pretty in much the same way we don’t see too many 90 year olds doing handsprings and cartwheels.
Age also includes behavior history, and the older the dog, the more habitual the behaviors. For example, a 12 week old puppy who started counter-surfing last week is a different case than a 12 year old dog who has been counter-surfing for 12 years. That doesn’t mean the 12 year old cannot learn not to counter-surf, it just means you’ll be breaking a 12 year old habit versus a 7 day habit.