I was reading "The Black Cloud" by Fred Hoyle when I got to thinking about Nightmare Moon's plan to eliminate the sun.
Now, in the My Little Pony universe the sun is not some astronomical object out there in space, it is something manipulated by magic. This means that there is not a night side and day side to the planet.  This is very important, as will become evident later.
Had Nightmare Moon succeeded in her plan, this "night that will last forever" would completely devastate the entire planet, rendering it uninhabitable to all but a tiny few creatures (assuming they exist) whose lives are not impacted by the sun's existence or lack thereof. Moreover, this horrible fate, the end of all pony kind, would happen in a much quicker timespan than might be imagined by the casual viewer. Allow me to explain with a little timeline.
First, it is important to note that this "forever night"  would be very different from an ordinary night. During the night the land surface cools down. This process is mitigated by the effects of the atmosphere. If there are clouds then less heat can escape and the land cools slower. On Earth there is always some point on the surface where it is day time, so part of the atmosphere is always warm, creating convection currents and preventing the entire atmosphere from cooling off. This is why the artic and antarctic never get too cold during their long, sunless winters, because warm air from the lower latitudes circulates, keeping the poles warmer than they would otherwise be. If the entire output of the sun was eliminated somehow (see note 1), then this saving effect of the atmosphere would no longer exist.
It is impossible to make accurate calculations without knowing the size of pony planet, but we can make some reasonable guesses.
A body the size of the Earth facing an endless night would rapidly begin to cool off. Immediately photosynthesis would stop, and small plants would begin to die as they used up their sugar supplies.
Within a week the surface temperature of the whole planet would reach freezing. The oceans, a considerable heat reservoir, would remain warm for a quite some time.
One month after sun and most plants have died or been eaten. Herbivoirs would not survive much longer. Ponies (being the equivalent of humans) do not seem to be capable of harnessing geothermal power, or operate submarines, as they seem to have 19th century equivalent technology (steam power). They would be able to burn wood, and possibly coal, for warmth, and live off of grain reserves (say a year's worth), but things would get very difficult very quickly. Many ponies would die early on, leaving the harty survivers to a long, cold, dark, lonley fate. The surface temperature would be arctic cold everywhere. Coastal waters would begin to freeze, but the opean ocean would remain liquid.
Six months after sun and the surface temperature is as cold as it ever gets on Earth, −80 °C (−112 °F). Only a few straggling scavangers will survive. If it can't live in Antarctica it can't live on pony planet any longer. Creatures would not only need adaptation to extreme cold, they would need adaptation to darkness.  The last of the ponies has probably died. The water in trees has frozen solid and the only surviving plant life is a few frozen seeds. Even the open ocean is frozen on the surface. Most sea life within the first 2 kilometers has died due to starvation. Deep ocean life continues to survive off of detritus falling from the surface.
One year after sun and the only things left alive are either immortal (Luna as Nightmare Moon, Celestia who has been captured, and statue Discord), or lives far below the surface. The deep oceans, warmed by geothermal activity  and insulated by over a kilometer of ice, will remain habitable to deep vent communities (tube worms, shrimp, etc., if they exist on pony planet), and bacteria slowly metabolising the rock near the mantle (if they exist ).
After that is wild guessing. Even the longest lived seeds would die after a few tens of thousands of year (maybe sooner, if they can't survive the cold). Global glaciations have lasted for tens of millions of years without freezing the oceans solid (although, the sun still existed). In the total absence of the sun, it would still be tens of thousands of years before the oceans froze solid. The only life would remain deep under ground, where the rock was still warm. The surface temperature would be the same as that of the Moon during night time, −238 °C (−477 °F). The atmosphere would have frozen long ago.  If pony planet is like Earth, geological activity will end when the outer core solidifies, a process which will take 2 billion years. Subterranian bacteria will have died long before this event, having used up all available water in the rocks. The entire planet will be dead, and all because a princess got butthurt because her subjects couldn't stay awake 24 hours straight.
1. As far as we can tell - unless Celestia does not "raise the sun" but "rotates the planet," which would have the same subjective effect. For purpose of this exercise I am assuming that Celestia actually raises the sun, meaning that when it is night time the entire planet is covered in darkness, and when it is day time the entire planet is covered in light.
It is possible that Nightmare Moon could blot out the sun by putting something between it and pony planet, like the Black Cloud. That object would need to intercept and absorb or divert all incident sunlight, and not in any way warm up, or there would come a time, eventually, where it would get so hot as to become as effective a radiant heat source as the sun itself. Either way, the effect would be the same, and the means of how Nightmare Moon eliminates the sun is unimportant.
2. "Forever Knight" was a TV series about a vampire police officer. http://www.youtube.com/watch?v=yPhIEG3JYtg
3. Vitamin D must be created through exposure to sunlight or ingesting something that had created it through sunlight. NONE of the latter survive. Life would entail a constant struggle to acquire this nutrient.
4. Volcanoes do exist, as has been seen on the show. The only question remains if dragons are the only creatures that live in volcanoes or if there are Earth-equivalent lifeforms like tube worms.
5. Ponies can get sick, so assumably there are many different kinds of bacteria.
6. If the pony atmosphere is mostly nitrogen, it would have frozen solid at −210 °C (−346 °F). Offgassing from volcanoes would still release carbon dioxide, which would also freeze, producing dry ice snow. Since volcanic activity won't stop for millions of years the atmosphere would consist of carbon dioxide waiting to freeze and trace gasses like helium.