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One can quickly note that the Church clearly opposes the freezing of embryonic persons, as the Church opposes the creation of human persons apart from the conjugal love of a husband and wife, let alone the subsequent freezing of such embryonic persons. This teaching is presented in the Church document Donum Vitae.
In addition, regarding the freezing of adults who are alive, given current technology, you would have to kill a person in the hopes of one day bringing him back to life, even though some have hopes of one day averting the killing of a person via the cryogenics process. So you have a violation of the Fifth Commandment, and, even if technological advances are made in the future, at least gravely jeopardizing the life of a person when there is really no hope of bringing him back to life.
Which brings us to the final category: preserving the mortal remains of persons who have just died, whether their head or their whole body. Here we run into the moral problem of not accepting the finality of death and thus attempting to play God—and vainly. Death is the separation of the soul from the body, and Scripture reminds us that we will have a particular judgment immediately upon our death (Luke 16:22, Heb. 9:27; see CCC 1021-22).
Cryogenics, or cryonics, is thus the vain attempt to retrieve the soul long after an individual’s death, as if you could pull the soul back from heaven or hell to do so. And so we see that cryogenics is an attempt not to accept death for what it really is: God’s definitive word on when it is time for a person to enter eternal life. Indeed, we were not meant to live in our current human state forever; we will one day be resurrected either to eternal glory or horror (CCC 1038-41).