Considering euthanasia is a good thing to bring up, Helen. Freezing of reptiles not a currently sanctioned euthanasia practice in the US, though. I think in the past it was. Here are the current AVMA guidelines:
https://www.avma.org/sites/default/f...al-1-17-20.pdf
Apparently, there is evidence that larger (>4g) ectotherms can become unresponsive but remain sensate until after ice crystals have begun to form in the extremities, which is presumed to be quite painful. Freezing is acceptable as a secondary method (that is, the one that ensures death), but the primary method has to be one that reliably renders the animal unconscious (which hypothermia is not thought to do in ectotherms).
"Hypothermia is an inappropriate method of restraint or euthanasia for amphibians and reptiles unless animals are sufficiently small (< 4 g) to permit immediate and irreversible death if placed in liquid N2 (rapid freezing) [...] because amphibians and reptiles lack behavioral or physiologic means of demonstrating pain or distress while hypothermic, generalized prohibitions on hypothermia for restraint or euthanasia are appropriate." (p. 94)
Most of the reptile recommendations involve injections; the only one that isn't rx is MS222 in a 2-stage process. I've not used this method.
I personally euthanize reptiles using approved physical methods that may not be appropriate to mention in the context of a long time pet animal. They're described in the linked article. If you want descriptions of these methods either here or via PM, @Spot, let me know.