Been looking more and more into this. This thread is a collection of personal experience and information from educated and experience sources.
Please note, this does depend on the depth of snow, but I'll try and make it clear what level of snow which skills are for.
Tent:
Firstly, when pitching your tent, you NEED to get the material as taught as possible. This is to allow the snow to roll off the tent. Also a second reason for this is because some tents actually use the taught material as an extra structural strength aid. The taughter the material, the stronger the structure. If the tent sags, you're looking at a situation where snow can build up on the tent. Imagine putting a few kilograms, of camp ruining material, on the back of your tent during the night. Not only could your pegs pop out and tent collapse, but the material could sag so far down that it sits on you and wicks the water onto your sleeping bag, wake you up, or both. Not fun.
Next up, but something you'll look to do before you actually pitch your tent, you'll need to make sure you have a clear spot to put the tent. If you only have a foot of snow, you can dig down to solid ground. If you have a few feet, it is easier to stamp it down flat. If you have a fair height of snow, I'd personally scrape off the top layer of fluffy snow, then stamp down the harder stuff below that. Remember, you want to get your base for the tent as flat as possible.
Thirdly, for tent pegs, you'll want something made for the snow. A 'normal' tent peg is made to go into the lovely grassy ground of most camping sites. For snow, you'll want special snow pegs. You can get them at many stores that supply ice climbing gear, and online you'll find loads. You can also use the good old snow-anchor system, but if you're only staying for a single nighter, the extra effort is boring, so I'd look at a set of snow pegs. Quick note, you can use them on sand as well.
http://www.amazon.co.uk/5Pcs-Inches-Alum...=snow+pegs
Fire:
Setting fire to snow is...urm...difficult haha. Setting fire ON snow...just as much of a challenge.
One of the simplest things to do is to dig down to the ground, and clear the area around your new fire-pit. One thing you could enjoy is using the removed snow to make snow benches or back rests. As long as you have enough down, you'll enjoy the ability to lounge out a bit.
If digging down isn't easy enough to do, and you have a fair bit of snow below you, you can make a base. The best way to do this is to just get a few logs, side by side, and let that be your base. Also, you can use this base to split wood via battoning, while building up materials for the fire.
One thing that will really help your winter campfire, fuel! Not a quick burning fuel (they can work, but I've never got it to work for me. If it works for you, that's cool) but a slower burning (solid) fuel like those little fire cubes you can get, or trioxane (recommended by Arctic Dave, but I've never found it in the UK...stupid Dave). This will give you a small working flame with which to build your fire onto. Please note, you do need to light it as you would any other fire fuel.
Sleeping System:
Snow = warm....? No wait, that's not right, snow is cold!
Even though snow can be used as a brilliant insulator, for sleeping mats...no chance! You want something much better. You'll want to get a good few inches off the ground/snow. You can go with just closed foam matting, but you'll need a lot to get inches off the floor. I've been recommended to sandwich materials. Start with foam, then use an inflatable matt on top of that. That combo, coupled with your sleeping bag, should keep you far enough away. If that's not far enough for you, there is always the option to go semi-native and look at using 2 layers of foam, but bulking an air gap between the 2 with small round logs and loads of debris between the logs. This makes a nice layer of air pockets, but also raises you well off the snow or cold ground. Not much fun cleaning leaves from the tent though.
I hope these 3 chunks of information are helpful.
Enjoy