The past 2 Travel Trailers I have owned were always covered during the Winter Months. Special Care needs to be done in order to prevent holes in the cover. Things like your gutter down spouts need to be covered with a tennis ball or pipe insulation. Any areas that the cover could snag on needs to be covered with something to prolong the life of the cover. Unless you can store it indoors or under a carport this is your next best option if you chose to keep it covered.
I spend more time preping the trailer for the cover than actually installing the cover. I just want to get a few years out of the cover so I'll spend the extra time covering items.
Hope this helps.
2014 Wildwood 300BH
2014 Ford Explorer XLT
2011 Ford F350 FX4