I've never used MDF but if you sealed it with a good exterior grade paint I cabt see why it wouldnt last a good while. I would stick with latex based paints just because they are all around safer for humans and animals.
Think you could get away w/ MDF for the walls etc, as long as you seal it with a good paint? I guess a follow up would be, what kinds of paint/varnish are safe for the inside of the coop?