Oh god, I have thought about this way too hard.
The way I figure it, Rorschach was transported not to another (MLP) planet but to our own planet (Planet of the Apes style) 1,000 years in the future. Veidt's plans only delayed all-out nuclear war. What humans survived the war itself were wiped out in the droughts brought on by the permanently atom-bomb disrupted weather patterns (perhaps the force of so many blasts also slowed the Earth's rotation, altering the day/night cycle). In this new, harsh environment, ponies with the ability to control the weather would have had an evolutionary advantage. Perhaps Princess Celestia was the first with magical capabilities strong enough to right the Earth's rotation speed, thus "raising" the sun. Certainly the pegasus ponies would have been able to clear the nuclear cloud cover and bring unpoisened rain to a blighted landscape, making it possible for earth ponies to cultivate the return of the plant life needed to sustain larger pony populations.
Hell, maybe the ponies as a whole are part of Adrian Veidt's fall-back plan--their unconventional coloring and proportions is certainly reminiscent of his past experiments in genetic manipulation (i.e., Bubastis). But whatever their origin, they survived and flourished in the face of atomic disaster, thus the cultural importance placed of the annual (Nuclear) Winter Wrap-Up.
ETA: Now with icons!