Growing season depends on your climate and growing conditions. Most of my Haworthia tend to do most of their growing in the fall and early spring, with a slow down because of cool temperatures during winter, but still technically in a growth period. They shut down in the heat of summer. This is what they do in habitat. If you're in a climate that is too cold for them to grow outside n the cooler months, you'll have to watch them for signs of growth, and take advantage of that. The growing season is most obvious in the 'window' types, (truncata, maughanii, badia, comptoniana, splendens, mirabilis and the other retusoids) because they not only green up and swell with water, but the windows become more translucent. The hard-leaved forms like Zebra may be a little different in growth season, but I think they also tend to rest during the heat of summer. For me, Zebra tends to be more tolerant of bad treatment than many other Haws, which is probably why I don't really notice their growth/rest cycles so much.
When dividing Haworthia, make sure that the wounds of division have healed over in the shade for a few days, then set the pups in straight perlite or a very high mineral soil mix, such as equal parts pumice, perlite and Turface, with a half part of a good potting soil mixed in. Avoid sand, it just fills in the air spaces between the other particles in the mix. Full shade isn't essential, succulents need bright light to generate the energy to root, but don't let the mid-day sun beat down on them. Morning sun until about 11:00 works pretty well. Plants which are under too much stress sometimes root very slowly, or not at all. Don't water them heavily, the soil only needs enough moisture to prevent desiccation of the new root tips. I mist mine lightly with a pump bottle in the mornings, and wiggle-test them for rooting every two weeks or so. It may take them a while to re-establish.
