Actually, they're most likely voles. Voles are often confused with field mice, but technically they aren't mice. Mice have relatively large ears and long tails, voles have small ears and short, stubby tails.
Voles are the bane of my existence, I've been fighting them for close to 20 years, ever since the old apple orchard across from me was clearcut and plowed one weekend to build a subdivision. Thousands of voles were suddenly homeless and many moved on to my property.
They won't hurt your birds directly, but are filthy, nasty things that spread disease, destroy crops, electrical wiring, vinyl and wood siding, get into stored food, and spread urine and feces everywhere they go.
You should start a control program right away. Poison bait blocks are good if you can place them where you KNOW other things won't get them. Traps work too, snap traps as well as glue traps.