The object of the ice bath is to put the person in a trancelike state. Werewolves will half-transform, and the trance will allow access to the subconscious. The induced hypothermia slows the person's heartrate down to almost none.
It is not a particularly safe procedure.
For some reason, the person is also held under the water during the bath, even though this is not necessary to induce hypothermia.
During Isaac's trance, his distress was able to affect the electricity in the Animal Clininc, suggesting that there is a magic component to the ritual itself.