Cleaning Deer Skin Gloves

I have deer skin gloves that I use for riding and they're sooooo dear to me, but they're so dirty now, & I'd like to clean them. I obviously can't use water because that would make them shrink to half their size..

What's the safest/best way to clean them?

Maybe just a standard leather cleaner. I use deerskin gloves but I get a new pair every year so I don't really worry about cleaning them.