Definitely field mice, not house mice.
Not many, but sometimes there is one looking at me when I lift the cover. From what I read, they'll be there because it's a great nest site, plus some food (vegetable peelings).
Websites talk about them as disease carriers... but I think they're so cute. Am I being naiive? Should we turn the heap over to shoo them away? Should we compost the vegetable peelings in a different way? Or can I just leave them until we forget about them & happen to turn the heap over, anyway.
We live almost in the country, if that matters.