I’m in Middle TN but I have a plywood floor in my coop with RubrCoat 57 on it. Pine shavings in the coop and nothing in the run. The 14x60 run used to be grass. But now it’s dirt (mud when it rains). I threw pine shavings out there and they just wash away when it rains.
I wouldn’t use the pine shavings if it will get wet. As others have said they will get soggy and take forever to dry out. I guess if I had a coop with a dirt floor I would just use straw or hay, grass clippings, leaves, twigs, just general yard waste. Then I’d turn it over every day or so, mix it up. The chickens are going to do a good job of scratching through it too.
What does your coop look like?