Don't take snow shoes. You will find enough of a boot track that they won't be necessary. If you go, please bring back pictures. I'll help you post them.
As for the chute, there probably is enough. It is enough of a north-facing slope that it will have a cover of snow.
The Whitney Portal road is open. Doug may open the store this week. Here's the Inyo N.F. Conditions web page:
