DEAD - but educated
At the risk of poisoning my theoretical self as I have already done with my actual self, I would stay put letting the car run to keep warm and hope for some other car to pass on the same road, paying attention that the exhaust would always have some breathing room to not get clogged.

I am going somewhere, why wouldn't anyone else be on a similar mission? Not to mention the slim chance of a snow plow coming by on the road I'm on or some other vehicle I could draw attention from.

Walking might help me reach my partner quicker but would not help in getting her back to our home at all. She is already freezing, her car way more covered with snow than mine already is, how would she make it back on foot with me in her condition? I would either have to carry her all the way back - which is unlikely - or hope for another car where she is, on the same road.

ALL I could do for her at arrival would be wrapping her in blankets and giving her some snacks and my own fading body heat. Plus spiritual boost in terms of hope, which should not be underestimated I guess.

Since I'm already dead, might as well take the risk of staying put to at least be able to reach her and eventually back home AT ALL. Although I would feel really really bad if three hours later I would still be sitting there with less gas and more worry.