It's a close call but from the pistol choices, I'd give a slight edge to the powerful .357sig.
The 10mm would do well but I'd use a Glock 20 or 20C or maybe a S&W model 610.
Gun writer Duane Thomas wrote a great item years ago about some of the major flaws with the 10mm round(for duty or carry use). The feeding & cycle problems would make me want a Glock 33 first.
If I was still in the US northeast, I would carry a .44spl, a .45acp or maybe a .40/10mm in winter months. I'd use a med or large frame sidearm(4-5" barrel).
A well made LE .357sig round like the Ranger T, Corbon DPX, Doubletap Ammo or Speer Gold Dot JHP should have the KE or punch to go through winter clothing & feed well in a sub compact Glock pistol.
Clyde