I often have snap traps set where the chickens, wild birds, and such cannot get to them to help control the mice. I also use a version of the Adirondack mouse trap. I feed mice caught this way to the chickens. They love them. That helps but occasionally the numbers get out of control anyway. Then I resort to the same poison, being very careful that dogs, cats, and other critters cannot get to it. I do not feed the ones that die from poison to the chickens. It’s possible the chickens will find a dead mouse from this and eat it, but a mouse weighs almost nothing, a chicken a few pounds. The dosage required to kill a mouse is very low compared to a dosage that would harm a much bigger chicken so I’m not real concerned if one does get eaten. Most mice don’t die in the coop or run anyway. I don’t like poison and only resort to it when the numbers get out of control or when I find I have several rats down there, such as right now and my live trap is not working for them. If you are uncomfortable using poison I fully understand that and you should not do it. Snap traps, live traps, and other traps can really help.
Now to your question. It is extremely difficult to keep mice out of the coop. Even if you take the feed up at night to discourage them, the chickens will spill enough in the bedding to attract mice. If they can catch them the chickens will eat mice, but mice are so quick my chickens often don’t even try. With the bedding there are usually a lot of safe places the mice can hide. I keep my feed in metal trash cans to discourage mice.
It takes a tiny opening for mice to get into the coop. That’s the really hard part. I don’t know what chicken wire you are looking at but if it is like the stuff they sell around here the mice would go right through the openings. Half inch hardware cloth would probably work, ¼” for sure, but all they need is a tiny opening around a door, window, vent, the foundation, or somewhere in the structure to get in. If you use wire make sure it is small enough that they cannot get through.
I don’t know what your run looks like, I’m guessing it is fairly small. A large run is a lot harder to make fully mice proof, let alone a lot more expensive. Chickens are sometimes kept on wire. You can put wire on the bottom of your run and they will be OK. Create a place of them to dust bathe by filling a cat litter bin or something like that with sand or dirt. If your run is fairly small, maybe add several inches of sand in the run to cover the wire.
A warning about wire. Not all wire is created equal. Due to manufacturing processes some wire might have sharp stubs sticking out that can damage a chicken’s foot. Normally these are on one side, not both. Before you install it, carefully rub your hand along it so you can install the smooth side up.
Good luck. Mice can be really frustrated. Try to keep the feed stored away from them and try to not give them paces to nest, like piles of trash or cavities where the chickens can’t get to them.
