Shooting may be a better idea.
Catching foxes with traps can be tough.Not as simple as dropping steel.
Winter adds a whole new element as snow and ice will freeze things up.
If you are hell bent on catching versus shooting, try snares.Much more functional in winter.
If your duck and goose hunting , try starting a gut pile near the den.Not too close maybe a few hundred yards.Set it up where you can snipe him from a couple hundred yards.
If you like the snare idea you can set snares on trails leading to the bait pile. if snaring versus shooting put baitpile in the woods versus the open for shooting.
Wait him out , if its cold enough he will be there.
I never saw a wild thing sorry for itself. A small bird will drop frozen dead from a bough without ever having felt sorry