The best defense is to shut down all openings on the upwind side of the barn/coop, and have them weatherstripped in one fashion or another so that snow doesn't sift through cracks.
This works best if you have a reasonable-size, not tiny, air volume inside the structure; and if you have a well-sheltered area on the downwind side to leave open for some ventilation. A very generous roof overhang plus strategically located windbreak structure(s) can be adequate; or if there can be a roofed and 2-walled 'porch' outside the duck entrance that would work too. The idea is to have ventilation openings into that sheltered area (which preferably faces south or southeast depending where you live), so that it is seldom if ever necessary to close *those* vents on account of extreme winds.
If you are stuck, for one reason or another, with a suboptimal situation where you just can't have really sheltered vents, then I would suggest closing the upwind ones and tacking cheesecloth or burlap over the others to reduce the velocity of the wind blowing in while still allowing *some* air exchange. Yeah, burlapped windows do eventually crust over with snow, but, you know, you can knock it off next time you're out there, the animals will be fine like that for a while if it happens.
(e.t.a. - snow sifting into the building would normally just be a management nuisance, not so much of a health threat per se -- the main thing to watch for is the drafts that *carry* the snow, as drafts plus humid-ish air (which is what you get in a storm) can cause frostbite problems... for chickens anyhow, dunno how vulnerable ducks even ARE to frostbite. With ducks you might simply have to keep them from blowing out of the coop, then change any extra-damp bedding after the storm passes?)
Does that help any?
As far as a door, I'd stay away from anything that opens downward the way you're describing -- it won't work in meaningful amounts of snow, will require lotsa shovelling at best, and will become hard to close when poo/bedding/snow/ice get mashed into the hinge area. Is there a reason not to use a conventional sliding door? Mount its tracks on the *inside* of the coop for security. A slider requires no shovelling for clearance and can be made pretty predatorproof if latched at night. If you're worried about depth of snow, either make the abovementioned enclosed porch type area around the door (as much size as possible), or raise the door up higher than your usual depth of snow in the lee of objects, if that is feasible.
Good luck, have fun,
Pat