On this old house recent episode they put in special bath exhaust fans that tied into the HRV. I believe they were mfg'd by broan.

That is a code violation in my area as a primary fan. You could use one as a secondary fan for the room I suppose, with a vent hood over the range. Many fans say in the spec/install books that they are not for cooking ventilation. I think because there is no prefan grease filter as well as some other configuration issues.

Blame it on the contractor, not the pipes themselves. In a cold climate, the exhaust vent pipes of any vent like the bath vent or kitchen vent should ALWAYS be insulated. Otherwise, when the moist warm air hits the smooth cool metal (and it should be rigid metal, not flex duct)you will get condensation, just like your iced tea glass in summer. You also need to check for moisture issues in and around the ducts since he didn't insulate. Running the vent may aggravate any moisture issues. It might be better to just let the taps run a bit to keep them from freezing. Believe it or not, we're having to do that down here well below the Mason Dixon. 9° this morning down in the holler.

The installation of a new vented fan isn't difficult if you hire a professional to do it. If it is 'very old' as you say, then I would recommend replacing the entire assembly: fan, duct & duct cover. Newer fans have 'dampers' that prevent cold air from coming back in & a newer model would vent your bathroom properly & safely as well.