Your chances of finding snow at low elevations this time of the year will be zero, unless an unlikely cold front turns up. Temperatures in Victoria at the higher elevations have been up to 10C. Not conducive for keeping snow on the ground.
Your best chance of finding any snow will be at one the ski resorts. Now, up until the first weekend in October it is mandatory to have chains that will fit the tyres of your vehicle when entering a ski resort. After the first weekend in October chains are not mandatory but advised, in case of ice on the road.
Further, the ski resort which has the best access for snow is Mount Hotham, where the Great Alpine Road provides easy acces via that road. Mount Buller and Falls Creek may have snow on the ground at higher elevations but it will be a long trek uphill to reach it. Mount Hotham is the highest ski resort in Victoria and The Great Alpine Road will give easy access to the summit.
Also, if you are driving a diesel engined vehicle it is good advice to fill up with special alpine diesel at one of the service stations near a ski resort.