Zion is iffy in winter, especially because so many routes to peaks are N-facing part of the way. Check out this cam
Zion Theater view NE. The mountains on the right are ~6800', and unfortunately, the camera is seeing the south sides. No snow visible now, but that can change in a wink. You can see Mountain of the Sun in that pic; and while what you see is bright and sunny, drop over the NE side of Employee Canyon to get to the route, and you will hit ice on class 3/4 rock.
Will you have a 4x4 HC vehicle? Not too far from St George is Moapa Peak in Nevada (on DPS list). How far are you willing to go into NV?
From Saint George, you can look N to Signal Peak; the S side is often fairly snow-free in winter, but once you drop over the rim, you typically get deep snow.
Many people X-C ski around the Bryce rim in winter.