Mossy Cave trail, at Bryce Canyon National Park, had our name written all over it. There are plenty of hoodoos to view, and it is at a lower elevation than most Bryce Canyon trails, so there is no concern of a toddler becoming precariously close to the edge (especially with snow and ice on the trails). This meant that our independent toddler could do the hike all by herself.
It is 0.4 miles to Mossy Cave, which does have some moss, but it also has huge icicles and reverse icicles (whatever it is called when an icicle grows upwards like a stalactite). The trail also takes you right passed a frozen waterfall, a water path in a canal created by pick and shovel wielding Mormons in the late 1800s to supply irrigation water to the communities of Tropic and Cannonville.
The temperature was in the upper 30s which made the snow on the trail a perfect temperature for walking (without crampons). We really lucked out with the weather, and the lack of tourists.