Do My Little Pony: Friendship is Magic ponies have coats?

Question

Real life ponies have long hair on their manes and tails, and shorter hair covering their bodies. Friendship is Magic ponies clearly have manes and tails, but do they have hair elsewhere? Their skin looks smooth, and the cutie marks look more like tattoos than colored hair. Or do the ponies have hair, and the cutie mark magically floats on top?

I'd be interested in answers for other My Little Pony generations as well.

nb: There's at least one canonical pinto-colored pony. But I guess that could be chimerism. Or magic.

Answer 1

Based on what we can see in the show, they must have some sort of "fur".

During the "Ponyville Confidential" episode, Snips and Snails get stuck together from some chewing-gum. Later in the episode, it is shown that to get free they had to shave-off their coats.

(note: the image here is taken after they get stuck again, in an attempt to drawn the attention of the other ponies)

Especially worth noticing is that in the scenes where Snips and Snails are shown without their coats, the cutie mark seem to be missing too. This would prove that the marks are "drawn" on the pony fur and not directly on their skin.

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Season 6 update
During the episode "On Your Mark" (S06E04) we hear Scootaloo say "I mean, it is pretty amazing how the colors just pop off your flank" referring to her cutie mark, so it is safe to assume that there is also some form of "magic" involved that cause the marks to appear on the pony coat.

Answer 2

So we know that Equestria is a magical place. That leads me to think that they do indeed have coats. Their cutie marks are THEIR magic. (And by that I mean each pony that gets them.) All of this leads me to think that cutie marks would likely appear with the owner's type of talent and change the hair color in the mark's area.