The theory is that lower SSN winters tend to have more blocking weather patterns, which keeps the cold air in place when moisture arrives, so you tend to get more snow and less cold rain.
It's not saying there's a link between solar activity and temperature (although of course there may well be one), and note this is specific to the northeastern USA, not USA overall or world wide. Nor is it a guarantee of increased snowfall for a particular winter, just an increase in the chances.
A scatter plot of annual snowfall for Hanover PA, which is the nearest weather reporting station to where I live, vs SSN:
