Mouse-icicle is not a good sign
If it's covered in frost or ice before it thaws, it's definitely going to get wet with time
What I do is use a tupperware container with holes in it, line the bottom with a sheet of folded paper towel and let them thaw out at room temperature for a couple of hours
Even if the rat gives off any blood or moisture, it will be absorbed by the paper towel
Thawing in a bag seals in the moisture and results in your wet mouse
Hope this helps