To be warm you need about three things, a tent, rollmat and a sleeping bag.
I'd recommend an inflatable rollmat as the best thing you can get for warmth. Non-inflatable foam ones are cheaper but less warm. If you want to combine a roll-mat and a camp bed, that should be even better since it will keep you off the cold floor but I can't fit one in my tent since it's quite low profile. The disadvantage of the inflatables is that they can get punctured but they'll still provide some insulation. If you're just going to a larp event, then you'll be fine but if you're planning on hardcore wilderness expeditions, then maybe consider something foam. Either way, look at Thermarest, their products are very good.
Tentwise, they should keep you out of the weather. You can get ones for very extreme temperatures but they'll be at extreme prices. One thing that will make your tent warmer is having other people in it! If it's a cold event, you'll feel the benefit if you squeeze 3 people into your 3 man tent. I'm taking my Explorer Scouts camping in January and I'll be making sure they're fairly packed in since it'll hopefully be a way of ensuring they don't die as I expect they'll have fairly crap kit and might die otherwise and we'll get letters of complaint to Bear Grylls (again). Note that if you end up sleeping in a big IC tent, you'll probably find it's noticeably colder so prepare accordingly.
As for sleeping bags, a 4 season sleeping bag is your friend, I also recommend a silk liner (much cheaper off ebay than in camping shops) for a very light bit of extra warmth. The other thing is that it keeps your bag clean so you only have to wash the liner most of the time - especially good if you wear a lot of makeup at events. Washing sleeping bags is a pain in the arse. A lot of the better sleeping bags have a lot more insulation on the top since they assume you're going to be sleeping on some kind of mat. Don't make the mistake of assuming the insulation in your bag will keep your back warm against the ground.
There are two broad types of sleeping bag, assuming you're already going for a mummy style one with a hood which you should be. There's down-filled any synthetic-filled.
Down will cost you more, probably be a bit warmer all told and pack down a lot smaller and be lighter. Down will also not keep its heat when wet and may require something like tumble drying to actually get its fluffiness (ie. insulation) back if you get it completely wet through. Synthetic will probably be cheaper, bulkier, pack down less well but keep its warmth if it goes horribly wrong and it gets soaked. Very much up to you and your use case.
Also, look for one with a foot pocket, they're good for a bit of extra warmth.
There are various schools of thought about how much you should wear inside a sleeping bag, some say it's warmer if you don't wear much since the sleeping bag is about the best insulation you're going to get so you want it close to you (I agree with this). Others say you should wear everything you've got (I'm not so convinced, and I think this is mostly the advice of people with crap sleeping bags or sleeping in bags not designed for the cold temperature they're using them in). I'd recommend that if you do want to wear stuff inside your bag, probably a set of thermals - thermal shirt and leggings (ideally merino wool) and wool socks is all you should go for since they're fairly thin and will let the bag do its job. A coat inside a good bag might do more harm than good. Putting that coat over the bag I've found is great if it's very cold. Equally, if you want to throw a few blankets over it, that will make things warmer too.
Hope that's useful.
Delvy note - Really great stuff by Drave there. I would remind that you lose most of your heat into the ground, rather then the air. That method to get you off the floor is really important. Having something warm, like a decent blanket, under you will be much more useful than one on top. A really big blanket that goes under AND over you is even better of course (I swear by mink blankets myself).