Not necessarily. They might begin to gray at roughly similar times, since hair color is under genetic control… but the same could be said about me and my non-twin brother.

Genes aren’t under a strictly timed on/off control – their activity greatly depends on the activity of other genes, which depend on environment, nutrition, stress, etc. Even if twins start out the same, a lifetime of this sort of cause and effect (and the fact that it would be impossible for them to live truly identical lives) would ensure that by graying-age, they would no longer be totally identical.

NO
BY THAT TIME THEY WOULDN’T BE IDENTICAL ANYMORE
UNLESS THEY ARE SIAMESE IDENTICAL TWINS

I’m sure they would. It is under partial genetic control. If one twin had lived a very different life, with more exposure to sunlight for example, s/he might go grey a bit earlier.