Some people in colder climates use heat lamps for heat. We are not in that cold of a climate so I just keep their water unfrozen (and normally put hot water out first thing in the morning) and have been known to feed them hot oatmeal, etc. on very cold mornings.
I've not gone through a winter with my chickens yet, so I don't have first-hand knowledge.
Choose chooks that are winter-hardy. I live in northern Wisconsin, where it can get really cold in winter. A friend suggested Buff Orpingtons, because they have fluffy, warm feathers, and smallish combs and wattles, so that's what we got.
Build a good coop. Make sure it has good ventilation that you can adjust, to remove the moisture the chooks produce. Also make sure there aren't any drafts, especially at the roost level where the chooks will sleep. Insulation is a big help. And, make it big enough to hold the chooks in all day when it gets really cold.
I've heard that people let their birds out into the snow as long as the temperature is above 30 degrees. You can also coat combs and wattles in vaseline to help prevent frost-bite.
[EDIT] I've also heard that giving them corn before they go to bed will help keep them warm because it produces heat during digestion.
Are there any alternatives to using heat lamps? We're off-grid, so DH is quite resistant about sparing any electricity for the chickens. What about propane or kerosene?
What do you think is the lowest temperature acceptable?
I don't think it's good to heat them. They need to grow their feathers in the cooler temps of the autumn, and then they should be fine over the winter. They are, after all, outdoor animals and, like wild birds, are perfectly capable of living in cold temps. As long as they have a draft free place to live, with plenty of food, fresh water, and living space, they should be fine.
I agree! If they've had exposure to the outside temps up to this point they are naturally growing hardy to the changes in temps. Like ebony said make sure their coop is draft free and if it gets really really cold (below 30 and stays there for awhile) you can stack hay bales up around the outside of their coop to help insulate.