I have spent a little time on Galveston Island and the surrounding area and I never heard about the snow and hurricane connection.
I had never heard the snow-hurricane folklore either but in a way it makes sense. I think it's just saying that in a year with extreme weather, there tends to be more extreme weather. More volatility, in other words. Lots of things in nature have quiescent periods and other periods with more variability. In fact, even the stock market acts that way (VIX and VXN are used as measures of volatility).