I have friends that winter dive and ice dive in wetsuits, but not many. The other factor besides what's been mentioned is wind chill. A moderate breeze can really drop the perceived temperature, so getting out of the wind into a tent or ice hut is important.
Gear can freeze on you, also. Warm water is useful to get clips and buckles undone.
Gear can freeze on you, also. Warm water is useful to get clips and buckles undone.