A drone could detect loss of communication with the pocket device (snow or falling into the ocean should be enough to do that) and start some recovery/emergency sequence. E.g. stop + try pinging the device, if there's still no reply automatically call 911 with an emergency and GPS location. Is there a 911 REST API? :)
It could also automatically trigger some sort of warning on a high-enough acceleration detection. Enough Gs that it's likely that you've broken an arm - send out several emails to other people who you've marked as being with you. Enough Gs that it's likely that you just feel a fifty feet - dial 911 directly.
obviously this is a less general approach; but i'd think the software could detect with reasonable certainty when it's subject was suddenly covered by snow.
Assuming you were still alive under the snow for a brief period of time you could hit the button then.
And if you weren't it could detect your heartbeat through a smartwatch and know you're in trouble.