Straw attracts mice, mice attract cats. Our neighborhood cat is doing a fine job.
I have several bales of straw for an archery backstop. When they get really old, they get tilled into the garden. There's hardly ever been a year when I didn't have this "mouse attractant".
A small lower winter entrance or mouse guard will usually do the job. I pity the mouse that tries to move in from spring to fall. 'Never had a mouse in a live hive, but they sure have made some messes in old supers stored outside.