Actually, hair loss is not a function of chemo killing cells (cells don't kill chemo, chemo kills cells), nor does it have to do with the similarity of of breast, hair, or other cells, other than how rapidly they divide, or the type of cancer you have.
Whether you lose you hair or not depends on the chemo drugs you use. Many of them are used to kill rapidly dividing cells, whether they are cancer cells, skin cells, hair cells, or blood cells. So if your treatment includes one or more of those drugs, you will lose hair.
Freezing your head will not cause mets, but it could inhibit the ability of your chemo therapy to kill existing cancer cells.
IMO, temporary hair loss is no big deal. It's a lot easier and safer to just let the hair go. You will have plenty of other things to deal with during chemo and worrying about hair loss just isn't worth the energy it takes.