The only thing I can suggest is what I did with mine.  I made it a separate room and put a real exterior door on it.  It may be overkill, but with walls properly built all the way to the ground, a ceiling, and a real door with a threshold, I have had no mice.   I had problems in the past with mice and vowed never to lose any more tack! I keep the door closed at all times, even if I am walking out and know I will be back as quickly as I turn around.  It was a little more expensive (I insulated the walls, painted, and put down a vinyl floor) but I have not had a mouse in it for over 5 years. 

My biggest piece of advice is that exterior, sealing door leaving no gaps for them to get in, otherwise, I don't think you will ever keep them out!!

I agree with the above post.  The best advice I can give you is about grain storage and saddle care.

Store grain in rodent proof containers, metal bins or trash cans work well as long as you keep the lid on them.  Rodents hate chewing through metal, but any other material is fair game.

Don't stack saddles on top of each other.  Storing saddle pads between stacked saddles is another big NO NO!

Another bit of helpful info is that rodents hate to climb, the reason you see chicken coops on stilt like legs is to keep rodents out.  Hang your saddles high enough that they won't shimmy up the stirrups.  Keeping the floor clean is another big deterrent.  I mean spray pine-sol on it weekly and you'll also see the amount of bugs drop-off.  Playing the radio can also keep them on edge.  Lastly, keep mouse traps on hand.  I'm not a huge fan of rat poison, our neighbor lost a cutting horse(very high dollar mare)to poison somehow but we never got the whole story.