There shouldn't be any snow at Rumpff Saddle as it is around 1,250m altitude. The snow line around Kosciuszko is currently about 1,700 to 1,800 metres at the moment, possibly slightly lower around the Bogong High Plains and will be disappearing quite fast now. Watching the snow cams you can see things changing quite quickly. I expect you will strike some snow once you get to Bogong High Plains and maybe a few drifts on southern slopes before then. If in doubt post some micro-spikes to Hotham Post Office. You shouldn't have any problems getting that far.
I am departing south-bound from Tharwa on 6 November and have just purchased some microspikes for the Main Range. I will post them home once in Thredbo.
"Perfection is attained not when there is nothing more to add, but when there is nothing more to remove".