You could try approaching them with rationality, although that angle just doesn't work with some Mom's....errrr people!
Try finding out what their specific objections to the mice in the freezer thing is. Is it a perceived health threat? Is it the idea of mice/rats in the freezer and the look of mice-icles and rat-cicles?
The truth is that frozen rodents are amazingly pathogen free, and are not "dirty" any more so than that left over chicken casserole that made it into the freezer from last night's meal. Or the frozen raw chicken/beef/sausage in the freezer.
You could try to alleviate their fears by double ziplocking and then putting the rodents in an opaque tupperware container so that no one has to see the rodents.
Bottom line though: Your parents may be irrational and illogical and no amount of facts may sway their opinion. Then dude, have them buy you a mini freezer for your room or the garage as someone else suggested.
When I was a kid I was denied any reptile pets much less the rodent in the freezer issue. Now I just ridicule people that act like keeping rats in a freezer is weird!!! 
Good luck!!!