I’m not sure if this is related, but my 2011 Ford Focus would idle rough (engine vibration), when it was cold. It would last for several miles, then quit. The dealer decided to change out the front motor mount. The rough idle (engine vibration) has quit for now - however, the weather has warmed up since the change out, so I’m not 100% convinced that it is cured, so I may have to wait till next Fall. (Oklahoma)
What I learned from the dealer is that the motor mounts are fluid filled, and can rupture / fail. Mine didn’t, but the cold weather may have made them more stiff, therefore allowing normal engine idle to vibrate in the car cab.