The snow is melting fast this year because of the rain and warmer weather. I haven't seen the Main Range this snow free at this time of the year for ages.
There are still snowdrifts on the track near Muellers pass but they aren't anything to worry about. Just don't cross them first thing in the morning when they are icy.
The Snowy river crossing below Charlotte Pass is fine, you wont have a problem. It may rise quickly if it has been raining heavily.
Because of the above I suggest you do the walk counter clockwise from Charlotte Pass. That way you can cross the Snowy straightaway and cross the snow drifts in the arvo when they are soft.
There is snow in the forecast for next weekend and temps will be dropping dramatically. Be prepared and have proper wet weather gear, warm clothing and a appropriate tent and sleeping bag if you are camping overnight. If the wind picks up it can get very uncomfortable.
Use this closer to departure to judge the weather -
http://www.bom.gov.au/places/nsw/thredb ... /detailed/Its a stunning walk. Enjoy!