I've had Ermine a.k.a. common or least weasels living around and in the house and garage, in Northern Wisconsin for years.
Only one winter, I had a pure white ermine run across the living room. Needless to say the dog was not pleased and gave hot pursuit which ended in the end tables being turned over, and the couch flying as my 100 pound lab felt he could fit into the same spaces as a 7 ounce weasel.. the ermine escaped of course, and the dog got a fast training session in house educate.
Although I saw him a couple times that one winter, I never saw a mouse in the house, and he was very kind about doing his toilet business outside as I never saw traces of his scat. Actually I left him alone (as did the dog after the first encounter) and he kept the house free of rodents. I wish he/she would return every year. Instead they live in the garage.
They are a facinating creature to watch while they hunt. They will move under the snow sneaking up on small birds. They pop their head up, get a bearing and suddenly they explode out of the snow and attack. A ruthless little critter, but very welcome around here.
To trap them is easy. You have chicken livers on a string off a branch about two and a half feet off the ground and place your traps under the liver. The weasels jump in the air grabbing the liver which weights the limb enough to lower them on to the trap.
There are other ways of getting them; with a drill, a tree, a chunk of meat, and a finishing nail sharpened to a very fine point.
There larger cousins, the pine martins, fisher, badgers, skunks, and wolverine are the ones you really need to be careful of.