I would bring it in and give it awhile at room temperature before turning it on.

Yup. This. Don't do anything with it until it's at room temp and dry.

Metal detector

This.

Interesting. Snow is less dense than water so I doubt the wetness is a problem at all.

The cold though may make glue or a gasket shrink or more brittle, so that’s a little concern for long term water resistance.

Not sure about cold and the battery. I’ve heard that heat is a battery’s biggest enemy. But certainly cold makes batteries less efficient.

I’d work pretty hard to find it.

If you do find it, don’t try to use it without replacing the battery. They’re not meant to be frozen. You might find that the cells are destroyed and your total capacity is a fraction of what it was. Not to mention lead to other hazards.

Perhaps an app like Wunderfind will help pinpoint the location, as FindMy over simplifies it while Wunderfind will let you see more real time data, if the battery is still alive.

Yes! That app really helped (found my phone). I was using it wrong the first time.