I find it easier to get a good night's sleep in the winter. It gets dark earlier, the snow is more comfortable to sleep on than hard ground, it tends to be quieter, and there is nothing as comforting as snuggling into a nice warm bag on a crisp night.
It seems unusual that your face would get so cold on a 15 degree night. Everyone handles the cold differently, but if your body is warm, usually your face is warm too, at least until well below 0F. Maybe your extremities were vasoconstricted for some reason. I would try all the usual recommendations for maintaining warmth, if you have not already done so:
Adequate sleeping system for the conditions
Exercise and have a snack before bed
Keep well hydrated
Make sure your base layers are dry
Good, snug fitting down hood
Warm socks or booties on your feet
If your face is still cold, do like Eric says and wear some type of facemask. I don't personally like breathing into a thick balaclava, so I use a sheer skullcap made from the sleeve of an old microweight base layer. This pulls down over my face and is thin enough to breath through comfortably. Don't breath into your bag or you will wake to a lot of condensation around your face.