Hi and welcome to the forum!
Many people consider June/July one of the best times to hike in the ‘berg.
Where are you from and what conditions are you used to hiking in? Could make all the difference.
By Northern Hemosphere standards I’d consider the Drakensberg winter mild. Night time temps can be anywhere from about 5 to -15C. They probably average at just below freezing or so, and the very low temps only occur during the worst of the odd cold fronts that come through, but are always a possibility and so should be taken into account. The cold fronts also tend to arrive and leave rapidly, but our weather forecasts for the area tend to be accurate, so there is some level of predictability. Day time temps are usually pleasantly mild.
There is generally more snow from early August to late September, but once again is always a possibility. Usually, snowfall is in the order of a few cm, but bigger falls do happen. I can’t say I’ve ever heard of anything much more than thigh deep. Snowy days are often followed by pleasantly warm ones, fronts usually don’t last longer than a day or two.
For some piece of mind, the rescue services in the Drakensberg are considered some of the best in the world. Also, as long as you have a good map and GPS, descending in altitude is often pretty easy as there are many passes off of the escarpment within reasonable distances of each other. Whether these may be iced up should be part of your planning of course (this includes the passes you take up). Ice axes, crampon etc might be useful, but many people get by without them too, especially you choose the easier passes to take.
For really in depth discussions and recommedations, maps, GPS data, etc., I’d recommend you register at and browse/ask questions over at https://www.vertical-endeavour.com