Brandon: You would need to frame for a roof mounted fan anyway, so it would be easy enough to rig it up for a cover. A simple type might be just a piece of exterior ply with holes at the corners, to match the location of anchor screws permanently installed into the fan frame. Then just use wing nuts to hold the ply in place. Line the edge of the fame with a strip of insulating foam and when the nuts are tightened, you would get a pretty tight seal. Or just cut a piece of 2" foam insulation to fit snugly into the fan frame and it will hold in place. BTW: It's always a good idea to install a by-pass switch on any hard wired appliance, especially one with a built in thermostat that might turn on when you don't want it to, such as a roof exhaust fan that's been sealed for winter.

What specific brand/model is involved? Difficult to answer accurately without knowing the details. Typically the dryer must be disassembled (rear or front panel) for access to change the internal 4" straight exhaust duct to the rear for a duct turned 90-degrees to the side.

The main reason is laziness and cost. What they should have done is installed an insulated 4 inch flexible duct to a capped roof vent. It needs to be insulated so the warm air does not condense in the winter and drip into the fan. Your old fan probably got rusty because there was no roof cap and the duct was not insulated.

Happy to help. I've had a bit of this work done myself, in two different houses. In one, I had a Fantech BFRK 100 installed. There was an existing bathroom exhaust fan that worked poorly but I didn't want to put in a new grill. With the BFRK, you take out the guts of the old fan, keep the housing in place, and then connect ducting that runs first to the Fantech unit located a few feet away up in the attic and then from it to the roof passthrough. I had that done by an HVAC contractor who was on site replacing HVAC equipment. I'm not sure they would have done the work otherwise, it was like a favor to me. The second one was the replacement of a 20 year old exhaust fan with light in a WC closet that was noisy and ineffective. I had that done by an electrician who also was doing other work. He needed to go into the attic to remove the old unit, connect the new one to the framing, put in a new duct and connect the power. It made a huge difference. That one also vents through a roof pass-through, important because we use it to vent the bathroom of moisture from showers and baths. Good luck and keep your BS detector handy. If other exhaust vents terminate in the attic, it's time to fix those too. Each duct run needs its own roof passthrough unless you're using a Y setup with one fan at the base of the Y for two locations. Be careful if so, those can be tricky if the duct runs from the rooms to the base of the Y aren't of equal length. As far as duct run distances go, the unit will specify the maximum distance. For my most recent job, the ceiling unit with light that was 110 CFM, I want to say the spec for the duct run was something like 60 feet. I wrestled with putting a wall vent on a gable end but decided to stick with the existing through-roof vent.