It's an old saying. But it's just that. Like looking at squirrels tails or the acorn crop. As a weather observer for now 30 years, there's absolutely no correlation.
November is certainly the descent into winter, offering the largest avg temp difference from 1st to last day of any month of the year. But if im going to play with patterns I'd rather hold a favorable look for December. It's so tempting to want to see that first snow, but I've almost become superstitious in recent years with early cold and snow shots leading to mild murky Decembers.