The full private key never exists. Not at creation, not at signing, not ever.
In case you missed it, Sovereign Money gave the most thorough breakdown of Frostsnap yet:
More bitcoiners than ever are securing their life savings outside their home and establishing sovereign inheritance pathways. Hugely successful week for Frostsnap at @BTC Prague.
Three years ago we attended @BTC Prague, jumping booth-to-booth to share our early prototype with friendly faces we'd only ever interacted with online.
This year we're back with the real thing: Frostsnap. Multisig made simple, with no single point of failure.