I can remember October 1976 being one of the coldest on record as was November and the Winter became the famed frigid Winter of 77. The following Winter had an early severe cold blast that brought snow to even the lower elevations on the 13th of October. However, the rest of the month was rather mild as was early November . Things changed abruptly after the 20th and Dec thru mid March was cold and snowy.
So, there are exceptions to the cold October =mild winter, cold November =cold winter rule. Of course, we are in a different era climate wise now and of all the years of record, odds favor the cold November cold Winter rule .