[1] This is known as "targeted temperature management" (TTM), and is part of the standard post-ROSC (return of spontaneous circulation) algorithm in ACLS (Advanced Cardiac Life Support), if you're looking for terms to Google.
What you might want to do is to cool the brain through cooling the outside of the head as well as through the nasal cavity.
Even if you chug a giant slurpee the largest effect on the brain temperature will be the cooling of the nasal cavity on it's way down.
We're talking about a naked, sedated patient (so they're already losing a lot of heat due to simple convection, and there's no heat being generated by skeletal muscle movements). The body's metabolism has slowed significantly, and it's producing anywhere near the normal level of "baseline" heat.
Afaik interest has been low in carrying around enough ice pack capacity to make this viable, and with lacking data for it even working, whereas head-cooling packs with circulating liquid through a cooler takes little space, cools way more efficiently and required no other maintenance after insertion into the patient in the ambulance (and is moved with the patient while continously working).
seems like a bold claim to me.
Because creating a cooling system to use on a body with a central nervous system fighting to keep it warm is just like central HVAC.
And yet, something as simple as ice cold water seems to work fine for this. You can cool e.g. even a heatstroke victim pretty quickly, without worrying too much about internal thermoregulation.
A heat stroke victim the body is fighting to cool itself and failing. You assist. That part is easy.
Getting the body to do the opposite of what you want is the hard part. ie. Cool down below basal body temperature, stop breathing to perform thoracic surgery.
It's exciting stuff, but it's definitely not widespread.