The thing about covering a run is that you have to account for the forces of wind and snow load. They tend to be stronger than most people expect.
Your safest bet is to make a windbreak on the upwind side of the run, just *outside* the run fence, using stacked strawbales, or plywood with its own supporting structure, or your winter supply of firewood, or snowfence-plus-burlap on a separate supporting structure, or etc. If you are real sure your run posts and fence are very strongly set and secure, you can attach burlap or plastic to the upwind side(s) of the run fence itself.
The top is trickier... hardly any runs that are not already built with solid roofs are built strongly enough to just put a roof on without beefing up the structure. (A number that ARE built with roofs are not built strongly enough for blizzard snowloads, either... see the yearly crop of threads on 'my run collapsed last night' each winter). So be very, very careful about how you approach this. I posted a thread a month or so ago, with a title something like 'go strengthen your runs NOW before they collapse under snow', with a lot of specific structural suggestions.
If you do end up putting plastic and/or roof on most of your run, make sure not to plastic-wrap the WHOLE run -- it needs quite a lot of ventilation, much more than a coop, to avoid becoming a humidity trap which not only is bad for the chickens when they're out but can also humidify your coop and cause nighttime frsotbite problems.
Good luck, have fun,
Pat