Like to Thank Jim and James for the reports
We have our first snow storm most often the last week of August then we are set up for the winter cycle about every 7-10 days a system will move by , this isn't saying we will get snow each cycle but we could and for sure the upper elevation moisture will be sleet/hail/snow and STRONG wind on the ridge.
The major storms are later now , most often end of the year, but as soon as you plan a Oct-Nov trip we may get 3-5' of snow . Road closed and no packed trail to follow. Most often people turn around early , because of lost the trail, very slow going and the load is very heavy for the gear needed.And just not enough time , winter trips can be 4-5 days in good weather on the main trail.
I say May and October are not for hikers,conditions can require full winter mountaineering. If you have the experience and the gear it can be done.