Great experiment, appreciate the comments.

Let's face it ... even IF the pea froze up ... how's that going to affect you?

Option 1: put inside shirt for a few minutes. Hopefully you'd notice and start doing this PRIOR to the SAR team walking past you.
Option 2: if it's that cold, you'll probably be trying to get a fire going. Said fire would conveniently warm body AND whistle.
Option 3: Whistle. You know, pucker up. Better than nothing. Though I assume you'd be pretty nippy at that point too and probably sound like a broken kazoo.

Seems the risks of a frozen pea are pretty far down on the 'what if' scale, with relatively easy fixes.