No, you are wise, not a sissy.
If you are interested in winter hiking, you may want to look at the southern half of the Arizona Trail: Winter is the preferred time of the year to hike this section. The full trail goes from Coronado National Monument on the Mexican border to Utah near Knabb. At present, the trail is nearly 800 miles long and parts of it are along old jeep roads. The southern Arizona part of the trail is largely upland desert although it also traverses the Huachuca Mountains, The Patagonia Mountains, the eastern Santa Rita Mountains, the Rincon Mountains and the Santa Catalina Mountains. If you hike at night you will share the trail with a few undocumented immigrants. You can easily hike 300 miles of the trail in winter and only occasionally have to route find on snow-covered trail. Water is usually available along the trail in winter but not in summer or fall. Once the trail reaches the Mogollion Rim, it is continuously above 7000'; it is snowing there as I write this. A GPS would be useful for much of the southern Arizona part of the trail; there are parts that are not yet well mapped. Check out the web sites listed below.
Three season gear would be quite adequate for winter on the southern Arizona trail if you have a sleeping bag good to about 10° to 15°F.http://www.greatoutdoors.com/published/hiking-the-arizona-trailhttp://www.aztrail.org/