I have a lot of experience with the Tahoe area.
The weather is entirely unpredictable that far out this time of year.
Tahoe has already had two small storms that dropped snow up high.
This fall, so far, seems to be cooler than typical... that could continue... or it could warm up... entirely unknown.
But it is highly unlikely that there would be enough snow to ski on by the 20th.
But maybe enough to make hiking difficult.
Be prepared for cold nights, cool/windy days, and high winds.