Is your ground frozen? If that were my run, I'd be converting it to deep litter. This time of the year, it's hard to get materials, but as the weather warms up, and more natural materials become available, you should be able to correct the issue over the summer. Things to add: bedding from your coop, grass clippings, hay, straw, garden debris, dry leaves, aged wood chips. Your goal: make a mix of materials that is at least 6" deep. Every now and then, toss a bit of scratch onto the DL. The flock will spend hours churning up the DL. It will absorb the moisture from rain storms, as well as keeping it from turning into a fecal dust bowl when the weather is dry. If you can cover part of the run to help shed rain, that will help also.