Anywhere up on the Mogollon Rim is great right now. The Rim Road (FR300) is closed, but I'm pretty sure the parking area at Hwy 260 is open, so you can use it as a trailhead. There's between 3 and 5 feet of snow on the ground depending on exactly where you are. (With a storm predicted for Saturday and Sunday, so keep the forecast close).
There's some nice views and relatively easy-going on the Rim Lakes Vista trail, and if you want to push the mileage a bit, hike the Meadow Trail down to Woods Canyon Lake.
The General George Crook Trail leads from the parking lot toward Woods Canyon Lake, but parallels FR300 about 1/4 mile to the north. Its an old roadbed, so its easy to follow.
The negative is that you may encounter some snowmobile traffic (especially on weekends).
Another option from that parking area is to head on the old road northeast to Willow Springs Lake, and hike around (or across ... its plenty frozen) the lake. There's not always a specific trail to follow, but it's a nice place to spend a couple of hours these days.
From the East Valley, I can get to the Hwy 260/FR 300 parking lot in under 2 hours, but I would plan on 2 to 2:30 if you're not familiar with the trip. Its about 29 miles east of Payson.
A little nuts.