You run the risk of ice tearing apart the cells of the rats. Technically you can refreeze them but the main issue is if you defrost them and they are damaged they are going to turn into mush when you heat them.

I doubt you will run into risks of disease, just mushy rats. In the future you can get a cheap styrofoam or other cooler and fill it with refreeze-able ice packs to keep it insulated.