Ok so I watched the video.
What they are describing is also known as TTM or Targeted Temperature Management.
https://en.wikipedia.org/wiki/Targeted_temperature_management
It works extremely well for the short term. The real trick here is to make sure that freezing people doesn't result in severe cell damage, because ice crystals are sharp and will rupture cell walls.

Assuming that can be overcome, i.e. you get cold but not frozen, what happens is the cold reduces the need for the body to process oxygen.
Because everything about chemistry is slowed down by the cold and you are made of chemistry.
Some animals do this naturally and even replace their blood with antifreeze naturally in order to survive the winter.
http://voices.nationalgeographic.com/2013/08/21/how-the-alaska-wood-frog-survives-being-frozen/
http://www.livescience.com/824-cold-hard-fact-fish-antifreeze-produced-pancreas.html

Excellent find! And yes it's a common tactic now in major blood loss, trauma situations, to reduce the patient's body temperature in order to slow down the damage from oxygen deprivation.