Covering an almost 1000 sqft run would be cost prohibitive for me. Tarps and things, no matter how tightly you think you have them stretched, sag ever closer to the ground with every inch of snow that lands on them, rendering my nice 6 1/2' tall walk in run a mere couple inches at best, especially with heavy, wet, March, April, and May storms. So I let the snow fall in the run, open the coop door so as the birds have the option of going outside should they choose and let them decide. After a couple days, at least one has had enough of being "cooped up" (pun fully intended) and the others follow.
Fortunately for the birds (and me, I hate snow far more than any chicken I have ever met) out here on the high plains, we don't usually have snow on the ground for too many days in a row. Eventually the sun comes back out and combined with our near constant wind, it melts off relatively quickly (at almost 5,000 ft, our intense sun and the Chinook winds off the Rockies, melts snow and ice even when the official temperature is quite a few degrees below freezing) so both me and chickens can get back our regularly scheduled programming in short order.