If the human brain (an astronaut’s brain in this case) is deprived of oxygen, irrepairable damage occurs within about 4 minutes. .. at body temperature. But under conditions of hypothermia (low body temperature), damage occurs much slower.

Hypothermic anesthesia lowers the body temperature to 68-77*F and allows blood flow to the brain to be stopped for an hour. https://en.wikipedia.org/wiki/Deep_hypothermic_circulatory_arrest

There is evidence from rescued avalanche suffocation victims that hypothermia is neuro-protective. https://www.resuscitationjournal.com/article/S0300-9572(16)30114-9/pdf#:~:text=Hypothermia%20is%20one%20factor%20in,make%20a%20comparison%20to%20drowning

There are anecdotal cases of downing victims immersed in cold water who have been resuscitated after 30 minutes. The longest time from hypothermic cardiac arrest to return of spontainious circulation is almost 7 hours. https://www.sciencedirect.com/science/article/pii/S0300957214005243

Back to the astronauts: If an EVA goes sour and an astronaut suddenly loses some or all oxygen supply, rescue and successful resuscitation would be enhanced by induced hypothermia.

Space suits have a Liquid Cooling and Ventilation Garment (LCVG). Passive cooling, as in positioning in the shadow of the ISS, would add to cooling effects.

Question: What policies and capabilities are in place to induce hypothermia for the purpose of reducing hypoxic brain damage in EVA astronauts? If not, why not?