1. feeding lots of sugary foods. Rabbits in the winter don't need extra feed, they just need GOOD feed and it's not a time to put them on a diet.
My rabbits get hay and pellets one day, a grain mix and pellets the next. Days alternate. The rabbits do well. In winters where the weather is up and down I add pineapple juice into their water. It seems to raise the freezing temp (so water doesn't freeze as quickly) and it encourages the rabbits to drink more.
2. Not breeding in the winter because the babies will freeze. Is there a risk that babies will freeze? Yes, but it happens less frequently than you might suppose. If momma does her job properly the kits will be born into a well made nest. AND one can bring babies in the house if its particularly cold out (they generally only have to come in until they are well furred). Litters of more than four rarely have to come inside.
So what do rabbits NEED in the winter?
1. recognition that they come with built in fur coats so don't make them too warm. No heat lamps necessary. They do need protection from the wind.
2. Good food. Not extra feed, but good feed. Not a time for diets unless you have a fat rabbit.
3. Water in bowls not bottles UNLESS you have heated water bottles. Give them new water at least twice a day.
4. Breeding is fine as long as momma does her job. Bring small kits inside for a week until their fur comes in.
5. Giving a box to sit in if rabbits are acting cold. Some rabbits don't get cold, others like to get up off the wire. So weigh out your rabbits needs.