Fluctuating RPMs in the during the three to four first minutes of driving in the winter?

That description sounds like a vacuum leak that shows when the engine is cold and seals up as it warms up. Those can be difficult to find without some testing. The first test would be to get a can or two of carburetor cleaner and use it to spray around the intake manifold and vacuum lines while the engine is cold and running and listen to see if the RPMs change in any area where you spray.

https://www.2carpros.com/articles/how-to-use-an-engine-vacuum-gauge

Once you find the leak it can be repaired. Common things are cracked vacuum lines or leaking gaskets.