Christopher's post is right on – that's a good summary of Eastern AZ wilderness areas. The Mazatzals and Superstitions might be good options to hike in the winter, especially if you're looking for some where with less snow than Pinetop. I was actually just at Reavis Ranch last weekend – wild temperature variations of about 45 degrees.
I would say the Catalinas, Rincons, and Galiuros might be a little far from Pinetop, but each person's willingness to drive is different. The Catalinas are great and I've hiked almost every trail in the range. That said, you tend to run out of trail or out of water pretty quickly there. Wilderness of Rocks is a good and popular trail in the Catalinas that you can link up with others; Lemmon Pools is nice to visit too if you can find them.
The Galiuros are a very remote sky island range. I spent 4 days there in February this year and saw a total of 4 people on my first day and no one after that; I spent another 4 days there in March last year and saw 0 people the whole time. If you go there, I would recommend the Powers Garden trail for your first visit: http://hikearizona.com/decoder.php?ZTN=17478
Powers Spring is probably the only reliable source of water in the Galiuros, although seasonal springs and water sources do exist.
One long trail close to Pinetop is the Highline Trail near Payson: http://hikearizona.com/decoder.php?ZTN=757
Another nice trail on the Mogollon Rim is the Cabin Loop trail: http://hikearizona.com/decoder.php?ZTN=797
And I've always wanted to hike the Blue River trail and go to Hannah Hot Springs: http://hikearizona.com/decoder.php?ZTN=678