From the 50s to the 90s we actually had a very strong connection between the couplet of a cold October plus a warm November and 40 inch plus snowfall seasons at NYC.
`1955-56, 1957-58, 1960-61, 1963-64, 1966-67, 1977-78, 1993-94
7 out of 7
1995-96 broke this pattern.
When I found this connection back in the early 90s and used it and the extremely hot 1993 summer to predict that 1993-94 would finally break our snow drought by comparing it to 1966-67, I didn't have access to seasonal snowfall totals from earlier than 1955 so I have no idea if the connection held even before then for very snowy winters like 1933-34 and 1947-48.