What part of the state is welcoming you ?

G is not what it was, still produces big bucks but not like years past.
I would talk with one of the guys living on the West side of Wyoming and pick their brains about areas that get less attention and have mature bucks. I'm thinking in the sage country maybe.
With time to scout and good public access you may turn up a dandy down in the lower country or foothills.
Late season hunts are always inviting but in areas like 128 now you have tons of spotters ands helpers with the hunters, lots of folks hunting the same areas and bucks. Lots of stories out from this years hunt about numbers of folks.
You might wander over to say MonsterMuleys and look at threads Wyoming mule deer hunting.

January is a brutal time to move to Wyoming, safe travels and welcome.