Can I put my climbing shoes in the freezer?

You can put them in the freezer, but I would ask for what purpose? Some climbers do put their shoes in the freezer to help get rid of odor causing bacteria which helps reduce bad smells, but that only helps to some extent, it might not completely get rid of the bad smell.

If it is for the smell, then yes freezing your shoes is just one step you could take (as long as the manufacturer of the shoes state its ok, shoes aren't cheap so I would always check!), but to really help eliminate and prevent the bad smell there are a few options, such as spraying your shoes after each session - my personal favorite as it's pretty simple and cheap and doesn't risk ruining the shoes in any way and really makes a difference. Besides that, also leaving your shoes out in the open rather than closed in a bad or in your trunk really helps.