I ship a lot of frozen animals. . .
If you ship a ton of mice (like enough to fill a large usps priority box) then you only need to pack it tightly with paper, shredded paper, or wrap the animals with fiberglass insulation. If you're shipping a smaller quantity, you will want to buy insulation or foam sheets from home depot or lowes, cut them to size to fit in your boxes, and make a cooler within the box, then pack tightly with rodents, and stuff any empty spaces with crumpled paper, shredded paper, or insulation of some kind. building your own cooler boxes like that is way cheaper. It's $5-$10 for a sheet of foam insulation, and it can make plenty of boxes in any size you need.
Don't add ice, dry or water ice. The only thing I could recomend if you needed ice packs are the goey bag ones (y'know? Like kids put in their lunches?) or fill water bottle with water, squeeze them a bit to allow room for expansion, and freeze capped.