1999 Ford Contour Rough idle, Stall, Cold Weather

I live in MN, owned for about 3 years and never had a problem in severe cold weather until now. It started last night when it was about -10. The car starts just fine then revs up to about 3000 back down like normal and when it gets to about 500 the lights/power dim for a flash sec and it either shuts off or revs back up. If I keep my foot on the gas it will keep running. If I let off it will either choose to die or rev up. After running (by me keeping my foot on the gas) for about five min it will run on its own for a couple of min (continuing the process of low rpms, light/power dimming, then reving again), for a couple of min on its own and then randomly shut off. It isnt until the car has been running for about a half an hour that no matter how low the rpms are it wont die. But once it has warmed up I had someone manually (under the hood) try to get it to shut off and it stayed running. I have heard maybe O2 sensor but I also know that there are many other things it could be. Any help at all would be greatly appreciated!
Merry Christmas!