Bath fan exhaust line length?

Hello all,

I have a set of three bath fans to vent outside the house. Two are easy. I can get out into the eaves in a relatively short run. The third one is on the second floor in a dormer.

The house is a steep-pitch cape with front and rear dormers. The bathroom dormer is a shed dormer. The shed dormer pitch is fairly flat.

The dormer has a flattish roof and the plumber suggested not venting through the roof because of ice buildup from the exhaust.

He suggested going out the side of the dormer with a dryer vent. It could work, but the only place it could fit would vent just above the main roofline and could plug with snow. (It's at the top of the shed, almost where the rooflines merge.) It would also build ice. And dormer valleys are already prone to ice damming and leakage. Putting a warm moisture source there in winter seems like a bad idea.

I'm thinking about running it down the wall and out the first floor eave. But it's a long run. How long of a run is okay for code (or practicality)? And can the exhaust run down or should it always run up?

Finally, can multiple bath fans share a common vent, or should they each have their own?

Thanks,

Peter