Mine survive below zero temps......although not that far below zero. I would think as long as they have shelter you can pen them in they'd do ok. Mine very rarely use their shelter. If I know it's going below zero...especially with wind chill or heavy snow I herd them into their house and shut them in. They'd rather be outside no matter what it seems.
Mine still go outside at -20 to -30... I don't use a heat lamp, just give them straw to cuddle in an have the door on the down wind side of the building. (And the -30 was with windchill in the -50 to -60 range). They do fine in North Dakota with no heat.
I would make a little house by taking 4 or more bales of straw. Put the bales in a square, touching eachother, then move one bale, and make an enterance. Then take a piece of plywood and put that over the top. I would also fill up the inside with lots and lots of hay and straw. Also, feeding them cracked corn in the winter helps them build up some fat for the cold temps.