Mine do not like snow. But with a covered run, you have an advantage, as it'll keep a lot of snow out, so they have space to walk about. I would affix a tarp to the prevailing wind side of the run, to help keep blowing snow and cold winds blocked as much as possible. This will help encourage them to go outside more. Buy a bale of straw or hay and toss some about every few days (rake it up if it starts getting yucky and put down fresh) in there to scratch around in. Hanging a head of cabbage in the run gives them incentive to come out... They will stay indoors quite a bit, but they still enjoy coming out for fresh air and treats...