Hanging a bear bag isn't just for bears. It's also to protect your food from other wildlife. Shorter and colder days are all the more reason to plan accordingly to protect your food from hungry animals that are just looking for an easy meal.
From Princeton's Outdoor Action Site:
“Bear bagging” is something of a general term used for hanging your food. There are lots of other animals (raccoons, opossums, coyotes, chipmunks, skunks, etc.) that will go after human food. In some cases you may be camped in locations where there are no bears, but still need to hang your food at night. The best thing to do is talk with local rangers about what the “critter” population is and what precautions you will need to take. In areas with significant bear problems, there may be permanent food hanging stands or containers provided by the park.
There may be some leeway in the winter according to regulations and park rules, but it's not worth the risk, especially if you are out for an extended stay and holding on to your food supply is critical.
This varies by region, but with changing weather conditions, there is no guarantee that the bears in the area where you just happen to be are in fact hibernating. Here in the Southeast black bears usually don't hibernate at all, considering the generally mild winters. They can be less active, but don't count on it. Other regions may be similar.
If the area you're visiting requires canisters, then maintain usage of the canister. If not, then still hang a bear-bag.
So as far as I'm concerned, yes, bear-safe rules still apply in winter.
Personal anecdote: I was backpacking on the Appalachian Trail in Grayson Highlands State Park near Mount Rogers in the winter several years ago. There was probably two feet of snow or more everywhere. We didn't hang bear bags. What got into our food? Wild ponies. Yep. Wild ponies. Who knew.
Caveat: All that said, there are always exceptions. Varying situations can often dictate what we do when actually out in the wilderness, especially in freezing temperatures. For example, if I'm trying to make camp as fast as possible because it came a blizzard and I don't want anyone to get frostbite or hypothermic, then a bear bag is not top priority. (I'm going to assume bears are also seeking shelter in a blizzard.) If me or someone in the group is taking care of a mildly hypothermic person, and they need to have food available to metabolize, then they can keep some food, while we hang the rest. Patient treatment takes priority. Sometimes you just have to weigh risks in less than ideal circumstances.