If they freeze the brain it will be mush when they thaw it. It's too delicate. [Yes, okay, if you must, insert zombie joke here] The water in the tissue will not only expand while freezing, a lot of it will turn into needle-like ice crystals that will puncture cell membranes etc. Too much damage to remain a working brain. You'd have to spike the blood with antifreeze or replace it for the time being. But that would cause too much damage just as well. There are single-cell organisms that can survive being frozen, but that's it.
Maybe inducing a coma and lowering the temperature near (but above, with a safety margin) zero could work, but probably only for a short time. This still would be a lot of punishment, and the human brain isn't really designed for that. Our brains are the most complex thing we know. They are used to, so to speak, being housed, immersed in liquid, in a protective sphere. Ever had a concussion? Brains don't like that. Sunstroke? Temperature control is an issue. Nasty stuff in the blood? Not good, so there are clever filter mechanisms to form a barrier (alcohol and drugs can get through to some extent, but that's neither here nor there).
I don't know what I'd do to try to survive, but I can't help the feeling that a body swap would only speed things up.
Next question: where do you get a suitable body? Does being an organ donor even cover that?
Bonus question: given that the body swap, against all odds, actually works - what will be the surviver's legal status and identity?