There are several forms of life that can exist without the sun. Recently in Israel a cave system was discovered that had been almost completely isolated from the surface for over ten million years. The creatures lacked color or eyes, and most either grew extremely slowly or fed on a bacterial slime that formed on the lower walls. The bacteria itself, it was found, was feeding off nutrients that seeped through the rock with trace amounts of water from the surface. Something like this could work.
http://en.wikinews.org/wiki/Scientists_discover_prehistoric_cave_with_unknown_lifeforms
http://www.scienceblog.com/cms/mystery-cave-in-israel-reveals-bizarre-ecosystem-10702.html
Then there are the microorganisms, some of which live in complete isolation at the bottom of the oceans around hydrothermal vents and others of which live under literally miles of rock, feeding off radioactive isotopes instead of sunlight.
http://www.livescience.com/animalworld/061019_otherworldly_bacteria.html
http://www.sfgate.com/cgi-bin/article.cgi?file=/c/a/2006/10/20/MNGJ9LT21J1.DTL&type=printable
Lastly, what about the Underdark or Underworld or however you wish to call it? It exists without sunlight. In fact, creatures from it take a penalty from exposure to sunlight. Yet some form of edible plantlife or fungus must exist for such a variety and number of creatures to exist there. Perhaps the plantlife consumes magic or radiation or geothermal heat or some combination of these - or something else entirely. Ants farm fungus using the corpses of their dead and any miscellaneous plantlife they remove from their homes (such as sliced off invading roots).
However it exists, some plantlife and animal life has adapted to living underground on worlds where an Underdark exists. The surface may die off - perhaps even the uppermost layer of the underdark - but the middle and lower layers will likely continue to exist. Note, also, that Dragons do not need to eat - or, rather, they can eat anything - including metal, rock, and ice if necessary - so they will likely survive on the surface after most other creatures die off. Aberrations may also continue to exist, as they may or may not need to eat.
Finally, there is magic to consider. If I recall correctly Daylight is one of the spells that can be tied to a Hallowed area. Some celestials might be willing to Hallow several adjacent areas. If a heating charm can be created that can be tied to a Hallow (and I can see lots of deities allowing this, as it keeps their worshipper alive), then small isolated communities will likely dot the entire world. As their population grows the area affected could be slowly expanded with more Hallowed regions. If the communities are near enough, then they might even send dog sled runners between them - for trade, for intermarriages, to organize to deal with a local dragon or aberration menace, etc.
So it is likely that the Underdark will become the main settling region, with some small locations on the surface also holding perhaps a village level population (at most, probably less).