Cause of bathroom fan leakage ?

I know this is very common problem and so with common problem, there are many posts and suggestions on internet and that made me extremely confused.

I live in NJ and my bathroom fan when covered by white(yellowish) plastic cover, leaks. This did not happen in the past in any winter but happened only last week when temperature was low. If I take out plastic cover from fan, then there is no water drop.
I checked attic and seems there is no insulation on the pipe fully.
Attached are the pics .

Do I have to insulate pipe till end ? Please guide me.

Thanks in advance.

 

Yes..... the duct should be fully insulated. Otherwise it will sweat on the inside and you could get condensation running back into the exhaust fan housing.

This what I use for exhaust fans that run thru a cold zone. Comes in different lengths.
Master Flow 4 in. x 12 ft. Insulated Flexible Duct R6 Silver Jacket- The Home Depot

 

Thanks. I will change it.

 

Why is it not just ran out the roof near where it comes out the ceiling instead of across the attic and what looks like out a wall, or worst out a soffit vent?