Joy, I haven't done it but since you're still waiting for a response, this is translated info from the park's website:
http://www.parconazionaledelvesuvio.it/grancono/index.asp#orari
"No reservation is required for visits to the crater.
Ticket service is open all year round including holidays except for security reasons in days affected by any adverse weather events."
Opening hours (All days including holidays):
January-February-November-December: 09:00 - 15:00
March to October: 09:00 - 16:00
April-May-June-September: 09:00 - 17:00
July-August: 09:00 - 18:00
I would suspect that it'll be quite chilly and possibly very windy and wet up there in November but people do it (see Nov. reviews on TripAdvisor) and seem to have positive things to say about late fall visits.