Pic - fantasticmrmatt.
Being cold can result in a very long, miserable night ... dawn can't come soon enough and your mind will be troubled with thoughts of hot showers all night long. It doesn't have to be like that though, with a bit of common sense and planning there's no reason why you can't *enjoy, rather than endure the coldest conditions.
1/ Beware the wind ... any form of shelter is better than nothing. Whatever you can do to get out of the wind will make a massive difference to how warm you are.
2/ Warm your sleeping bag. Get warm before you get in your bag, jog on the stop, jump up and down, have a little dance ... anything to warm you up. If you do, your sleeping bag will hold that heat and you'll be much warmer.
3/ Don't get wet ... obviously that's easier said than done but if you do get wet, change into something dry as soon as you can. Damp, wet clothes will strip the heat from you very quickly. Condensation in bivvy bags can also be a problem, it's not uncommon to wake up cold in the early hours because your sleeping bag's damp from condensation and quickly loosing its insulation.
4/ Camp high ... in cold, still conditions beware of valley bottoms. Cold air will sink into them and remain there. It's often a few degrees warmer on the higher ground.
5/ If you're sleeping on frozen ground pay more attention to insulation beneath you than on top. Double up on sleeping mats or lie on your pack, dry bags, etc.
6/ Once you're cold it's hard to warm up ... put on extra clothes, hat, buff, etc before you start to feel cold.
7/ Don't sweat ... in freezing conditions it's still possible to sweat while you're riding. Once you stop or start to descend that sweat is going to cool you down rapidly and possibly even start to freeze.
8/ Eat, as simple as that ... food will warm you up and keep you warm.
9/ Sleep on your side, the contact patch between you and the ground will be much smaller if you sleep on your side rather than your back.
10/ Anything you can put between you and a clear sky will be a bonus, even sleeping below low branches will help slow down the amount of heat lost into the air.
* This may be stretching things a touch but at least you'll be alive and miserable.