Well,
@andrew_s has given a lot of useful detail.
I'd disagree with
@Heltor Chasca about showers. I think they're a great way to warm up.
I enjoy winter camping but the biggest issue I find is the lack of daylight. I'm not a fan of cycling in the dark. Winter camping is about the only time I plan a route and actually stick to it. So my advice is to know where you're going and have a backup plan just in case.
In the same vein, something to keep you amused on the longer nights. A Kindle is invaluable. Or podcasts on your phone.
I also tend to cycle slower in the cold, so keep that in mind when planning how long it will take if you are similar.
I carry a flask as a part of my cooking gear. Very handy for having a warm drink inside the tent with none of the faff of lighting a stove (I'll fill it after cooking dinner).
I've used my trangia at well below zero with the winter attachment. A bit fiddly to get the hang of, but it works. I've also seen people use a tissue paper "fuse" to light the method. Can't vouch for it personally.
I have an insulated water bottle. I've used it a couple of times with hot (not boiling) water as a hot water bottle.
A pee bottle saves leaving the tent in the middle of the night. Make sure you fasten it properly 😀
Fresh (wool) clothes for when all outdoor chores are done, especially socks. Never skimp on socks! For really cold weather a wooly hat, balaclava or something similar.
Consider a foil emergency blanket under your sleeping pad to boost insulation.
If the ground is wet I'll put on my rain pants to pitch the tent. It stops whatever else I'm wearing getting wet or muddy.
There are liners available to boost sleeping bags. I used to have a Merino wool one. Very effective, but not durable. If you're likely to exceed your comfort level for your sleeping bag consider a second bag instead of a liner. Probably cheaper.
Jumping jacks or something similar if you get too cold.
Condensation is the big issue in winter camping. Wiping the fly is well and good if you can easily remove the inner. If not, a footprint covering vestibule space can help, as will as much ventilation as you can stand.
Long, cold days on the bike can be improved with tinfoil around your toes.
Merino glove liners can be a big help against cold hands, especially if wet and cold.
Throw your cycling clothes in the sleeping bag with you (unless wet), they'll be nicer to put on in the morning.
Packing is best done slowly and carefully. You don't want any dampness transferring, especially if there was condensation.
I find cold mornings the hardest part of winter camping! My sleeping bag is just so cosy! 😀
Enjoy!