Sorry to hear they didn't "sound off", or wander back. Can't address human pred,, though unless turkey run/coop is easily accessed (visible) from road, or someone found them wandering? Call all neighbors and let them know to give you a call if they see them.
Could they have gotten spooked by a pred (though I'd think all the turks would have taken to wing) Jakes/toms will go wandering to A. find hens, B. spar for breeding rights. However, this would be more likely to happen from late Feb. on, not in late January. If penned up, it is the hens that are most likely to take to the wing (almost always in order to go nesting in an unauthorized location)
Since there is snow on ground: Pack up a bag of Black Oil Sunflower seeds/Scratch, etc. Begin searching for turkey tracks just outside run and start spiralling out from there. Sure, the jakes/toms fly, but they prefer to remain on the ground when not roosting.. Place piles of seed on downed snags/clear area of ground with foot and place pile. Clearings/along banks of drainages, etc. Hopeful you will at least be able to ID tracks before it snows again and you have to start search/baiting all over. Also, if home at sundown, go out and listen for yelps/breaking branches (usually what they do in process of roosting).
Yes, they can get lost. However, our neighbor had a good sized flock, some years back. There is a little over ten acres of dense underbrush/hardwood and cedar between properties. Late Feb. and two toms and three hens hoofed it over here through the woods, spent the day on opposite sides of the 6ft. fencing trilling challenges, hens whining, etc. - then their flock wandered down to the road, at sundown, and marched, single file, up the road to their property. Bring this up as it is A. very unusual to have the jakes fly over fence, even if challenged by toms/smitten by hens B. If "imprinted" on "their" "range", they usually don't get lost - particularly if within sound of the vocalizations of hens.
Sure hope someone didn't get in run and take jakes! When searching - call out loudly with whatever vocalization you know to make jakes "gobble" (ours hate my whistling tunes).
Don't give up on search, or calling. Check/replenish your "seed pile" trap lines for at least a couple weeks (there have to be big turkey tracks SOMEWHERE nearby).
Best of luck!