You'll have a long dark night. So either bring along a radio, podcast, audio book, book of some sort.
You can get a safety cage for putting a candle in, and hanging in tent. Provides light and heat.
Consider some charcoal and an oven foil tray. You can cook and keep warm at the same time.
If you have a heat source consider a tarp and groundsheet so you're not cooped up in the tent too early.
Consider which way your tent or bivvy face. A winter sunrise on frosty ground is a delight.
Beware if hollows or low ground, chance of just being sodden or getting flooded.
If you wander deep into woods away from the road before dark. Make you you mark the direction back out to the road.
Caves can be good if you have a fire.
Bird / wetland centre hides are rarely locked and make a good place to sleep in winter. Make sure you don't use the one nearest the car park. Other nocturnal may be happening in the nearest one.
Don't forget there are bothys in Wales, Lakes, Scotland.
Bus shelters on quiet roads work well in winter. Again have a heat source.
Be organised, easy to lose things or kick them into the undergrowth in the dark before you settle.