Buy Traps
Collect enough gold pieces throughout the game to purchase the Mouse DeathBot or the NVMRC Forcefield Trap. These traps will not only catch mice in the mountain region such as the frozen mouse, but can also trap mice in the Burroughs region as well.
Use the Right Bait
Use cheese with a high attraction rate to improve the chances of attracting a frozen mouse in one of your traps. Standard cheese tends to only attract diamond or gold mice. Cheese with a high attraction includes Brie or Super Brie.
Stay in the Mountain Area
Stay in the mountain region as this is the only area to catch not only the frozen mouse, but also the frosty snow mouse and the abominable snow mouse. Be sure to stock up on cheese before entering the mountain region so you won't run into unnecessary traveling costs. You can purchase cheese at Moustachio the Charmer's Shoppe.
Capture a Ninja Mouse
Capture a Ninja mouse. He will be carrying a piece of the map which will unlock a new hunting location in the north where you may find a frozen mouse. You will be exposed to more Ninja mice once you achieve Master rank. The Ninja mice are also attracted to Brie or Super Brie cheese.