Now is the winter time in Brisbane, but the lowest degree in Winter time is only around 7-8 degree. Thus, we cannot see the snow.
However, you can go to SkatingAt Festival(which used to call Winter Festival ) to have a snowy winter.
From today to 9th July 2017, a giant ice rink and ice slide have setup in King George Square. I believe you can skate in there. But you need to pay the entry fee, Adult $26, Children (8 to 13-year-old) $19, Kid (3 to 7-year-old) $12.(Buy online ~20% off).
Also, there are some food trucks next to the ice rink. They offer some hot foods, which is the best for the cozy winter, such as German Sausages and wood fired pizza.
That sounds cool, I think you should not miss this event.