Really, really rough start

This morning it was awfully cold out (I'm now in the Sierra Nevada foothills for a little vacation), and something pretty strange happened when I started my car. It started ok, but the RPM's struggled a little bit directly after starting and the car started shaking violently for about 5 - 7 seconds. The issue cleared up after that, and the car drove just fine. I also noticed this same thing happening (but to a lesser degree) on cold mornings in Southern California, and also when the car hasn't been driven for a few days).

Yesterday morning, and later in the day today, the check engine light came on for about 45 - 60 seconds. It went away after that, and drove fine both during and after the light was lit up.

Any ideas? I'm thinking maybe the TPS

Thanks a ton!