I had a house infested with mice, last winter. Hope it will not happen again. With two cats, there still were mice. I think it was the dry conditions that made it possible for mice to tunnel towards my house, and then get into it via double walls with insulation.
One mouse in a cage may be cute. Two mice equals lots of mice in just a very short time. And, a mouse has no bladder, so it leaks urine all the time, when and where ever it goes. Yuck!