Buttermilk will work fine, as will regular milk, just keep changing the milk as it fills up with blood. And keep it cold while you do this. In Missouri I have taken a lot of deer, as have my father and brother, and as such I've had the pleasure of helping make it many times. One of my mothers favorite way to feed a family of 5 was to crock pot a deer roast with a small beef roast (along with the normal carrots, potatoes, onions, etc), this helped tame the flavor without having to soak it first.
Last year I made some venison stew out of a deer that was extremely gamy. I cured that by soaking it in milk, changing the milk every so often till there was no more blood in it, and make some great stew out of it. Took it to the families get together at Christmas and none made it home.