Not exactly the target audience since I don’t run, but I have a husky that requires a lot of exercise, so I walk a lot, every day. Rain, sleet, -30C blizzards, we’re still out there, walking. My only exception is when it’s warm enough that he might get hurt, that’s when we do shorter walks.
I just suck it up. We have to walk. Make sure you dress appropriately and make the best of it.