NE winter? What NE winter - ? Maryland is south of the Mason-Dixon line, and technically the south (or Southeastern US) - same for Kentucky and the states between them - lol. Not a whole lot of salt thrown down between there and Kentucky, as it doesn't get all that much snow and ice. Some years, being much worse than others. Maybe in the mountains - I dunno ... On those bad occasions - especially in SE states, you really shouldn't be on the road with a trailer anyway ... people down that way don't have a clue how to drive in the winter-shit. Your bigger concern are the sand and rocks that will be thrown up on the bike, which always the case, worse in winter.
Solution: enclosed trailer. OK, if not an option: Wax the fook out of the thing - and keep it waxed. Wash often, as in, pretty much any time its exposed to the slushy stuff.
These folks claim to have "trailerable" bike covers. I've owned a couple of their covers, but have never used one on a trailer (and frankly, I don't think the ones I have should be considered all that "trailerable" ...).
Good luck!