I had heavy duty tarps over the run, and they did very well. But we're going to replace them with polycarbonate sheets this fall, so that it's lighter in the run. It was dark and gloomy last fall/winter.
Another thing I did was to take shower curtains and zip tie them over the west (prevailing wind) side. I went around the SW and NW corners for about 3 feet. This cut the direct wind, but there was still plenty of ventilation. Some people build removable panels to put up for the winter. I might do that next year.
I also ran an exterior grade extension cord to the run and used a large heated pet water bowl to keep their water thawed.