I'm thinking of putting some gravel in the run to fix the problem. I live in MN with lots of water and obviously snow. Thoughts/Suggestions?
Here is a good article on this problem: https://www.backyardchickens.com/a/how-to-fix-a-muddy-run-chicken-coop Hopefully this gives you some ideas. Gravel might be good.
I put leaves in my run. It helps keep the smell down and keeps it from getting slick. It also gives something for the chickens to scratch around in & makes good compost for the garden.
I would buy a bale of wheat straw. It will adsorb the moisture and smell good too. When it breaks down then add more. When the old straw needs cleaning every few months then make a compost pile with the poopy straw. Chicken manure /straw compost make a really hot pile. You can never go back with gravel. It doesn't stay clean if you throw a lot of snacks in the run. It will get muddy and you will have to add more.
We also have this problem. We are considering digging down 5 or so inches. First laying down three inches of gravel, landscaping cloth over that, and then 2 inches of builder's sand on top. Do you see any problems with this?
You'd need some pretty sturdy landscape cloth for that. The chickens will probably tear it up. I wouldn't put plastic down either unless the area is sloped away from the coop.
Digging down might be fine if you work through some of the problems that others will bring up, but at the same time, a solution of laying down straw like others have suggested works decently, too. I know when it rains, the rain will travel down the tree trunk and still wet the area, but you could also help it a little more by giving the chicken run a covering also. That will at least help with the direct rain hitting the ground of the chicken run, then you just have to find a solution for the run off from the tree.
Skip the gravel and plastic....go with mix of sizes and shapes of dry plant materials. Here's a great description of contents and how to manage organic 'bedding' in a run or coop...and there's a great video of what it looks like. https://www.backyardchickens.com/t/1037998/muddy-run-help-please#post_16017992 You being in MN I gotta ask........What are you going to do when you have 2-3 feet of snow on the ground?