Uh.... Did you sleep in there already? I am afraid to tell you that unless you wear an appropiate sleeping bag you are going to be cold. That snow cave is dug out at ground level. The entrance is at the very same height as the sleeping surface. I am at work now so I can't really elaborate but try to google a bit about snow caves. To be heat efficient you need to have a cold trench below the sleeping surface so it works as a trap preventing drift and warm air lose.
The trick is to find a big and stable snow bank and dig first horizontally and then up. The problem is that you need ideal snow conditions and lots of snow. Fresh snow will colapse and ice will be hell to dig out. Also the smaller the entrance, the better, but you also need elbow room to work with a shovel.
That snow cave will provide some protection from the wind and trap a bit of air if you block the entrance (be carefull not to suffocate yourself, poke a sky pole through the roof if you decide to block the entrance.
BTW... just in case you were wondering....
Been there... done that. We got caught by a storm in the Alps at 4000+ meters (like over 12.000 feet I guess). Even we were familiar with the whole theory... we had a not so funny night in there. We ended up digging with the cooking pot (remember what I told you about elbow room?) and chopping some ice spots with the ice axes. We took turns because it was very tiring. I was carrying a 0ºC rated sleeping bag and temps dropped to -17ºC. I slept fully clothed and wasn't as cold as I expected (I have endured a few worse nights). Next day we crawled out of our hole, climbed to the summit and went back down pretty much thrashed.
Mikel
PD: The metal sheet in the lower portion of the picture is the heat reflector from the stove while melting snow.
PD: I just re-read my post and noticed that I might have sound like a smart-ass. Didn't mean it. Sorry if I sound like that.