Since you're military, consider the Fort Huachuca hunt down in Unit 35A next to the town of Sierra Vista...you'll have very good odds at drawing a late December hunt. I'm retired Air Force and take my kids down there for the junior hunt in November. My brother is active duty Army and was stationed at Fort Huachuca for 6 years...hunted on post every year.
Things to know about the Fort Huachucha hunt that can be a little annoying:
Register your firearm(s) with the MPs.
First day of your hunt, must sign out in person at the Outdoorsman Center (they open at 0500). Can sign out by phone afterward.
Must sign out to a specific a Game Management Area to hunt in (the fort is divided into several areas known as GMAs)
Game Management Areas are subject to closure due to weapons firing or training
Be out of the field by 1930. Sign in by phone.
If you harvest an animal you may field dress it, but not quarter or bone it out. You must take the animal to the Outdoorsman Center where it is weighed, photographed and fill out a short questionaire. The fort's wildlife biologist tracks this information. Then you can butcher the animal.
My son Nick got a nice little 3x2 buck for his first deer two years ago on the fort. Impressed me with a 383 yard shot across a canyon using a 7mm-08. Last year my daughter Claire shot five times at a buck using a .243 for her first hunt, but missed. She was trembling with buck fever, though. I'm hoping she has better luck this year.
There's black bear, mountain lion, turkey, javelina, coati mundi on the fort. Had a black bear come up to within 20 yards from my dog and I last October while we were scouting.
No matter what unit decide to hunt in Arizona, best of luck to you!
-Paul
Air Force - Fly, Fight, and Win.