I agree with most of the other posts I've seen on here...I have no problem using live animals to feed pets, but I don't see any point in making things unnecessarily stressful for them before they go off to complete the circle of life, so it's good to hear that you're looking for alternative methods. Using CO2 to kill mice is most likely a very stressful way for them to go. Humans, dogs, rats, and most other animals have chemical receptors in their nervous system to detect excessive CO2 levels, and it gets pretty unpleasant for them toward the end if they are euthanized with CO2. I was unable to find anything that specifically said that mice are the same way, but I'm 99% sure that they are. CO is a much more humane way to go about it. It does the exact same thing as the CO2, but they are unable to detect CO so (in theory) it's much more like going to sleep than feeling like they are asphyxiating. I have no anecdotal evidence from mice saying that they preferred the CO though. I have no clue how available compressed CO is, but they probably carry it in the same places they sell CO2.
Residual chloroform in the mice may (over a long period of time) become harmful to your pet, but I have no evidence to back that up for sure.
As for freezing them while they're alive, I imagine that that is incredibly painful. While a little pinkie that doesn't have much mass will definitely freeze pretty quickly, I bet it hurts pretty badly before they drift off.