We have seen lots of class C's and class A's towing trailers with bikes.. We wintered in Benson, AZ several years ago with our 31' Class C and 2 Harleys and there were a couple of other rigs with Bikes only besides us. A class C toy hauler and a 5er toy hauler. When the weather was really bad we all rented cars if we had the need. We just lived with it most of the time. Good rain gear + good leathers are required. We use an open bike trailer but have covers for the Harleys. Most RV places we frequent have separate storage areas for trailers and such just ask them.
Dave