These little critters will want to make a toasty nest in your beehive, especially when winter comes around. While they won't harm your bees but they will definitely do damage to the honeycomb. They chew through the frames and comb to create their winter nest.
To keep mice out, install an entrance reducer. These metal guards have holes small enough to keep mice out, but big enough that bees can still travel through. You can buy the entrance reducers or you can make your own with a piece of angled iron, by simply drilling the guard into the lower entrance of your beehive.