A mob that falls from a great height while it is in a minecart will not take any fall damage as it normally would while falling normally. I tried this with a chicken and it fall at the maximum rate. I thought this would be the only way to get chickens to take fall damage, as they normally flap their wings and slowly float down.
No mob (including player) takes fall damage while in Minecart, but when leaving minecart.
Chickens never take fall damage.