I haven't had a problem with a heavy infestation of mice at my own barns, but have at a couple where I would go to work.
Western saddles I hang by wire from a rafter through the gullet. English saddles I hang by wire from the rafters through the irons. Pads can also be hung by wire from the rafters as can bridles and buckets of brushes. Metal cans for grain, blankets, extra pads, halters.
One ranch lined their feed room with aluminum sheets. Completely.
I don't mind using poison, but one has to think about barn cats and dogs, or other wildlife eating the poisoned mice. There may even be restrictions in populated areas for that reason.
Beyond removing any possible food (including wheat straw with too many grains in it), and eliminating as much material and location for nests, I have used traps. Blasted, dirty little critters.