I am going out on a limb here, and someone more knowledgeable please chime in, but I have had similar issues in real cold weather. It would take longer to come on than normal. I am guessing there is a relay for the headlights that activates after the machine starts, and your relay is frozen. It should work fine once it warms up. I guess this is a somewhat common occurrence with the fuel pump relay. Some people just carry a spare in their coat pocket where it is a little warmer, and swap out when needed.
On a side note, I had an 06 Nytro with that issue. Also nothing in the spedo was working. If you lost your spedo/gage cluster, I would say you did blow a fuse. That was the issue with mine.