intend to run bath fan thru roof

I'm researching and "about to do" some attic insulation. I'm taking out the bath fan duct that currently runs from my bath fan to the soffit as I am reading all the reasons why I should do this and intend to run it thru the roof. This is the roof duct I intend to put in as it has "a rise" and less likely to have snow buildup blocking the exhaust.

Home Hardware - 6" Black Roof Exhaust Vent

My attic is directly over my bedroom and bath.......My question is ... With all this work I am doing to insulate my attic won't cold air "come in" from this vent and come down into my bath (cold air falls /hot air rises). Yes it has a damper but I cant see that some little "non efficient non air sealing" damper will stop cold air from migrating its way down. Wouldn't i anticipate putting my hand in front of this bath exhaust fan (WHEN NOT RUNNING) and feeling cold air entering my bath??. Am I not now introducing a path for cold air to enter my bath?? My duct is 4 inch but this is 6 inch. I intend to attach a 6 inch to 4 inch adapter to it (any problem with that??

 

Generally the fan has a damper and most roof hoods like you linked have one as well so you have double protection against drafts. Still, the dampers are a loose fit and are not insulated so there is a good path for cold to come inside. Unfortunately with a vent fan there is not too much you can do about that.

If you think that's bad consider when you are using the fan. You use electricity to run a fan to force your precious heated air out of the home. And, for every cubic foot of air you blow out, cold air must somehow seep back into the home to replace it. Vent fans are one of the worst things for energy efficiency but they are a necessary evil to prevent moisture damage in the bathroom.