A friend asked me a very sensible question about starting to compost in the winter. Here are my 2 cents:
You can start composting at any time, dead of winter or high heat. In the winter, not much will happen, except that you'll keep your food scraps out of the trash. If you're generating a lot of compost, it will stay warm and will most likely attract rodents, so keep that in mind. If it's just you and one or two others adding to an outdoor composting bin (or pile) it'll take you a while to accumulate enough compost for it to heat itself up and start decomposing. If you're hoping to use the compost in the garden, I would suggest bringing in some neighbors into the composting or it'll take you a long while to get enough compost to actually make it decompose fast enough and be usable. Compost likes to be 50% carbon (dry things like leaves, wood shavings, and straw) and 50% nitrogen (wet things like kitchen scraps, lawn clippings, and manure), and damp (though not wet). If it smells badly, add more carbon. In general, you'll tend to be short on carbon.
A sensible urban alternative to outdoor composting is starting a worm bin. here's my tutorial:
Get a large rubbermaid tote (like a big craft bin). Drill 15 or so holes in the bottom and top of the tote. The bottom holes are for drainage and the top for ventilation. Lay down mesh (such as a window screen or you could use cheesecloth or burlap - but you'd have to replace that from time to time) so the worms don't crawl out. Put the bin on bricks or styrofoam blocks or whatever you have lying around and set a tray under the bin to catch excess moisture. Alternatively, you could drill a larger hole (about 1/2 inch to an inch) about 1/4 of an inch up from the bottom of one side of the bin. Cover the hole with mesh and stand the end away from the hole on a brick so that the excess moisture drips into a little try out of the hole. you can use this moisture as fertilizer too. Some people swear by it. My jury, however, is still out. Don't worry about mesh on top. Worms don't like air or light.
Shred some newspaper or brown paper bags, moisten this mixture, and put it in the bottom of the tote. throw in a handful or so of soil and put a wooden or plastic divider with holes big enough for worms to get through in the center of the tub so you have 2 compartments. Put food scraps in one half of the tote and add worms (see below for more info on worms). Store your tub in a warm cabinet or closet. Worms aren't very active in the cold and can die if temperatures drop below freezing.
When all of the food has turned into worm castings (which is basically a nice, clean soil - this should take a week or two depending on your worms), put fresh food scraps in the other side (you can keep a typical compost collecting bin on your counter in the mean time), give the worms a day or two to switch sides, and take out the castings, which are ready for use in a garden or for indoor plants (you can store this in bags, totes, or buckets until the summer). If it starts to smell, drill more ventilation holes - it shouldn't smell. Replace the newspaper from time to time and the screen you're using (if it's burlap or cheesecloth) to keep the worms in.
The best kind of worms for a worm bin are Red Wiggler Worms. Put a post on Craigslist that you want them for free, and someone will be sure to oblige.