The snake's various biproducts are deterrent to mice, however. As are the scents associated wit cats and other mouse eating predators. (Unless the mice are loaded up with toxoplasmosis gondii germs anyway.)
You might want to describe where and how you place your traps, and what you bait them with. May people don't properly place the traps.
Mice have very bad eyesight. Like- REALLY bad. They mostly use their sensory whiskers and senses of smell to navigate. This means the favor being right against walls, and in tight fitting spaces, where their whiskers brush the walls. That is where you should place traps.
Again, mice have great senses of smell. Smasher style traps need to be thuroughly cleaned after a kill, or other mice will avoid the trap. Also, despite what cartoons and hollywood say, mice don't like cheese. They prefer seeds that are rich in oils, like sunflower seeds, or peanuts. Peanut butter is the usual bait of choice, but sunflower seed cake will work well too if you can find it. Always wash your hands aggressively before setting traps, and especially after emptying a trap that's made a kill.
If you don't have pets, (and thus don't have to worry about scent marking), get some canned "deer repellent". It has compounds in it that are formulated to mimic the scents that carnivores leave, which deterrs deer. It can also deter mice if formulated for rodents as well. (Squirrels and rabbits). If you have pets though, it can cause them to start scent marking and peeing inappropriately, so use with caution.