So, you've already had the idea of "Hobbits' hair goes white in Winter" and "What if: if it gets too cold Hobbits hibernate." Let's take this further:
These things don't affect Hobbits in the Shire all that much as temperatures rarely dip below -5°C or above +25°C. [I know that doesn't make much sense given how far inland the Shire is, but Tolkien was making it out to be Middle-Earth's [insert England here.] Also, look at the mountains around Mordor: does that seem like the invention of someone who cares about sensible geography? So yeah mild enough in the Shire.]
But these changes REALLY take effect in places with much wider seasonal variations.
What if in very hot places Hobbits tan, and then tan much, much darker than humans? What if their hair gets thinner so as not to over-heat? If it gets thicker for warmth in Winter, why would it not go the other way?
What if Frodo, as he was nodding off on Caradhras was going into hibernation?
What if Hobbits can withstand insane seasonal variations? +50°C -- still trucking along just fine, has become nocturnal to cope. -40°C -- has made a burrow, is in hibernation, fine.
What if their pupils can contract and dilate much further than humans, allowing them so see fine in both very bright and very dark conditions? What if their pupils can change shape: becoming cat-like in dim light?
What if Hobbits are terribly efficient at dispelling heat from their bodies? They sweat more than humans, maybe blood goes down to their feet (which are exposed) and cool that way. [I'm thinking like how, isn't it that African elephants pump blood around their ears and flap them to efficiently cool down.]
On the other end of the spectrum, Hobbits are very efficient at warming back up. They're round and fat as a form of insulation, and usually just plain old shivering will warm them back up. The Fell Winter took so many Hobbits not because it was exactly too cold for them, but rather due to the lack of food they burned through their natural insulation -- and that is why they froze.
What if -- and I actually reckon this is more-or-less canon -- Hobbits can survive much longer on very little food compared to other species, as long as they don't get too cold? Hobbits eat 7 meals a day by nessisity. But they can survive on barely one, as long as there's nothing else actively killing them.
What if Hobbits can take anything nature throws at them? Sure they won't be all too comfortable, but they'll get on with it. Their bodies just ADAPT to it, for the most part.
@stardryad -- if not the inventor of snowy hobbits, the one who got the idea going.