What is a bearing buddy? Never heard the term before. Every trailer I've ever had the bearings were in the hub.
As far as mice, lotsa luck. I haven't found anything that consistently works. Peppermint oil not at all, mothballs sometimes, but not always. Someone on a classic car forum suggested charcoal briquettes. Never tried them.
I suppose if you have a cavity they nest in the steel wool trick will work (as long as it doesn't short out the wiring), as well as to block entry points.
Best solution I've found is a cat.