Modern New Englanders have satellite technology and the Weather Channel to help us, but our regional forebears weren't so lucky. They had to rely on almanacs and their own senses to predict when snow was coming.
They also had a storehouse of folk knowledge to draw upon. For example, it was believed that you could predict snow by looking at the bottom of your tea kettle when you took it off the stove. Snow was on the way if the bottom was white. Similarly, you could be sure a snowstorm was coming if the wood in your fireplace hissed a certain way. Sadly, there's no record of what that certain way is.
The logic behind those two methods is a little murky to me, but these next three seem more practical:
1. When it starts to snow, look at the size of the snowflakes. Large flakes mean the storm will be over soon. Small, fine flakes mean the snow will continue for quite a while.
2. If the snow on your roof melts off, the next storm to come will be rain. If the snow on the roof blows off, the next storm will be more snow.
3. In the same vein, if the ice on the trees melts off, the next storm will be rain. If it is blown off by the wind, more snow is on the way.
Unlike the kettle and firewood methods, these three seem like they're based on some empirical fact, which is the air temperature. If the air is warmer, the flakes will be bigger and the snow will melt off trees and roofs. It's still no guarantee the next storm will be rain, though, because a new cold front could always move in.
Of course, you can always throw practicality out the window and indulge your irrational side. It was believed that if you make a wish on the first snowflake your wish will come true. And if you're the betting type, writing down the date of the first snow storm will guarantee that you'll win a bet sometime that winter.
I culled this information from Clifton Johnson's What They Say in New England (1896) and Fanny Bergen's Current Superstitions (1896). It looks like 1896 was a good year for folklore books!