The first schnauzer that I remember well was Krikit, a dog of champion blood and a great little family pet. She loved to hunt mice. When we lived out in a rural area, she prowled the yard for any sign of rodents, and was lightning fast at getting the unlucky pests that came into the house. Krikit once dragged a 10-foot long piece of gutter pipe from the back fence of our property up to the edge of our back porch. We couldn't imagine why she would have gone through all that effort until we looked inside the pipe. There was a mouse nest in it. All we had to do was tip the pipe up and let the rodent slide out. Krikit was there, ready and waiting for us humans to do our part so she could finish the job.
Frisky hunting ground squirrels in Colorado
Larry and I owned a schnauzer/Scottish terrier mix named Frisky. She had the instinct to hunt rodents but we discouraged it, as it generally extended to any small creature, including baby birds, lizards, and toads. In her early days, Frisky did manage to attack and kill a rat in our backyard, but we eventually convinced her to curtail her barbaric habits. We knew that we'd succeeded when Frisky found a small white hamster in our yard, a former pet that one of our insensitive neighbors had tired of and just released. Instead of the usual result when terrier meets rodent, we found Frisky gently licking the terrified little critter. The hamster was subsequently rescued and given to a good home.
Our current dog, Periwinkle, is a fox terrier, and she certainly thinks that any animal smaller than she (and sometimes her judgment of relative size is not very accurate) is fair game. The key word here is "game" as she doesn't seem to be hunting as much as playing. She tries to get at squirrels, opossums, and birds, but it never appears that she is intent on slaughter so much as just wanting to have a good time with a playmate. Once fox terriers were no longer being bred as hunting companions, they were obviously selected more for their playful personalities. Everything is a game and no chance to play should ever be declined. Peri will play all manner of games until everyone else gets too tired, and then she will try to persuade us to continue. She's had the chance to chase ground squirrels in Colorado and mice in the fields in Wisconsin. She's not very adept at it and has never actually caught anything, but her tail wags uncontrollably while she is engaged in the sport of the chase. In our current home, we don't have a problem with mice, but I sure wish Peri would learn to hunt cockroaches...