...or you can be like my buddy Chris Ruff and sleep by the fire with a greatcoat and a blanket, waking up throughout the night to gather more firewood to put on the fire. xD He's as tough as nails, even when it's below freezing.
You have to learn how to sleep outside or in the cold when you're reenacting. Such things as:
Try not to sweat before you get to sleep and dry your feet if they're moist.
Take off your socks or footwraps and wrap them around your midsection when sleeping.
Wear a cap when you're sleeping to keep in the heat, even if it's your kepi, slouch hat, service cap, or whatever you have. There's a method behind the madness of the nightcap.
Make use of all of your uniform to keep warm. If I have a blanket, I lay down my greatcoat and cover myself with the blanket. I'll also drape my tunic / coat over my head and tuck the sides under my shoulders. Also, the great thing about a greatcoat is you can stick both of your feet into a sleeve and fold in the end of the sleeve to keep in the heat.
Layers = heat retention. That's why straw is so damn useful. If you are able to get some sort of layer between you and the ground, excellent. A lot of the time the ground will actually suck the warmth out of you.
It'll be miserable, but livable. No need to get hypothermia during the night or be so cold and miserable you're crying to figure out a way to get warm.