That will probably work!
How much snow do you have? Ours will come out if we make paths. If it’s light and fluffy, a leaf blower or broom can make quick work of it. If it’s more, we shovel them an area, and eventually snow blower paths.
Only one of my girls absolutely refuses to touch snow. She'll stand there and roar at me like it's my faultMy girls stay in the coop if so much as one snowflake falls. Then they refuse to come out for days. Their food and water are in the coop, heated water buckets and enough food to last for a week. But I feel bad that they don't come out and I envision them picking on each other out of boredom. Tomorrow, I'm going to put straw out in the run to cover the snow. Hopefully they will come out then

I have a good layer of leaf litter in the run (not as deep as I'd like but good enough until I can collect more) and any soiled bedding goes straight into the leaf litter as well. Decomp process keeps the ground in the run relatively warm compared to the air so when snow manages to blow into the run, it doesn't stay long with the leaves and the girls scratching around. I imagine straw would work the same!