Why does car sometimes not Move during cold.

Why does car sometimes not move during cold weather, but works fine in warm weather?

Key data:
1) car sits all day or all night
2) in cold weather (20 degrees farenheit or colder) the wrench and engine light come on
3) car will start and heater will blow heat
4) will go into gear, but will not move at all or will eventually go forward after 30 minutes of idling
5) if turn car off and on after it moves, the car will move up to 50 miles per hour with engine light on.

6) Same car in hot weather will run fine- no engine light, no wrench.
7) the odbII reader shows ERR when connecting to DLC. The DLC fuse is fine and the cigarette fuse is fine.
8) unable to get error codes due to ERR
9) car ran fine today with warmer weather.

10) net net: runs fine 99% of time; just in cold weather it may or may not have the wrench and engine light come on; thus leading to 30 minutes of delay before I can move forward and go.

thoughts?