1990 Lincoln Mark VII starter problem sometimes it will not

I got a 1990 lincoln mark seven that when I start the engine when its cold like only in the winter time, that the starter starts the car all right but will not disengage from the flywheel. It does not do this in the summer time or when its warmed up in the winter time. After starting the car in the winter the starter will disengage after about 20 or 30 seconds. Could it be the starter drive or the starter solenoid on the fender well? Thanks Alot. ED