Re: live mice in house!
Welcome to CF!
Unfortunately, the ONLY way for you to control what she brings into the house with her from outside, is for you to control the door and only allow her inside without 'guests'. I had to do this when our first cat brought in a mortally wounded vole who escaped under the microwave cart and died, stinking up my kitchen! I cleaned everything; counters, cupboards, drawers, pantry, oven, microwave and fridge before I thought to move the microwave cart and discovered the vole.
I began keeping the door closed and calling for the kitty or listening for the kitty to be ready to come in, but with me controlling the door we never had to worry about him bringing his catches inside again. If you are concerned about her being out all night in the cold, call her in at the same time every evening so coming in at that time becomes a habit. If she doesn't come in, she gets to spend the night outside.
If you provide a snug little covered bed for her, as long as the sleeping area is out of drafts, is big enough just for her, has a top so she can preserve her own body warmth with a small opening to keep heat loss to a minimum, she should be just fine.