I think old fart is more of a state of mind than a specific age... and also relative to the perceived audience.
I'm 38, and generally think of myself as being 'young-ish,' despite the loads of gray hairs. (At work, I have the largest number of gray hairs, even though I'm the youngest by about 5 years.)
But I'll occasionally call myself old, old fart or curmudgeon if I think I'm showing my age.
Normally I'll do that when I'm talking to (or think I'm talking to) someone 15+ years younger than myself.