Would you let a little mouse live in your house?

Ashley
Okay so we have an uninvited guest who has mad himself cozy in my laundry room. 
I don't see the big deal letting him stay. As I'm sure he'll leave after winter. I'm a big animal lover and see no harm in a tiny field mouse. I think he sleeps in this drawer right beside the washer. I put food in there because I thought for one, he must be hungry, and two, maybe it'll keep him out of my kitchen. 
My fiancé has bought a trap and set it up and I found it today and I set it off and put it up. I don't want the mouse to die especially. What should I do? Is he going to bother us by staying there for the winter? He's so cute. 

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