You rarely (if ever) have one mouse. If you see one, chances are you already have a family living in your home. Pretty soon they'll bring in their cousins, uncles, aunts, neighbors...etc. And then they'll multiply.
The mouse poop could have been from a scout mouse, brought in from the cold to find a nice place to colonize. Perhaps one of your cats snatched it up before it was able to return to blab about the nice place it found.
If I see/hear any indication of an invasion of mice I'll take a glue trap and wedge it in between my fridge and the cabinets. The dogs can't reach it, but I can still see if I take any prisoners.
They can come in through the weep holes in brick, scurry their little bodies under doors, through walls etc.
Hondo Von Dopplet L Bauernhof "Hondo"- GSD
Lilie's Tug McGraw "Tug" - Golden Retriever
Maggie - Mini Dachshund (Rescue)
Lonestar Pivo - Texas Blue Lacy
Ashe - Barn Cat
Katie / APHA