I have a 4" metal dryer duct in the joists of the basement and in the cold Wisconsin winters frost develops on the duct to about 8 inches into the house. Then when the dryer runs it melts it and water drips inside the basement.

Will insulating the 4" metal dryer duct help? Or any other suggestions.

I have all of the fins in place at the exterior of the dryer vent.

Yes doing that will help. I would suggest that the fins be checked from time to time to be sure they are working. Sometimes they freeze causing the air to back up and can cause longer drying times and possible fire.

But the insulation will help prevent this.