a warm sleeping bag or quilt rated for at least 5-10degC BELOW the coldest temperatures you are expecting
an insulated sleeping pad / mattress (NOT an air bed!) with an R value above 6 (or as a minimum, above R4.0)
a shelter such as :
3 season double wall tent if weather is great - has less condensation than most 4 season tents
4 season double wall tent if you want more protection
you can even just do tarp camping under the stars
clothing to suit the conditions and use layers to avoid getting sweaty
boots should have removable inners so you can dry them out and they don't freeze overnight
beanies of different thicknesses
gloves of different thicknesses
a stove to boil water and bring extra fuel than what you think you will need
water (you can use snow but it will use up a LOT of gas to get it to melt and boil! - doing this may need 2-3x more gas than usual)
snow shoes if you will have thick snow and you plan to do some walking
a wide shovel to shovel snow to create a tent site or sleeping site, etc
a Nalgene bottle which you can fill with hot water to help keep you warm at night or use it to dry out wet socks placed on top of it
the usual personal beacons etc in case things go wrong
consider a stool - it's not fun sitting on freezing rocks or ground!
some may consider trying out a hot tent but this is not really necessary, although if the weight is not an issue, it is a gamechanger in winter!