Not a bad idea. I've been meaning to get some Chore Boy's copper wool (brass wool?) for my soldering iron.The sell the foam that has pepper mixed in. Hopefully the mice will not like pepper. And also copper (maybe its bronze or brass, non rusting) wool as steel wool will rust and look ugly.
The steel wool at least was tucked behind the vinyl siding and should not be getting wet--it's also mixed in with that foam stuff. It'll give out some day I'm sure but stopping the critters was job #1.
I did some reading on the foam that is rodent rated, but some reviews indicated that some critters will chew through it anyhow. Better than regular foam, better than nothing, but perhaps not 100% effective.