For weather forecasts the meteorologists use a snow gauge to measure snow accumulation.
The snow gauge is set at places such as airports, the weather stations location etc.
Then the information is tied into a computer system to show the meteorologists the amount of snow that has fallen.
They also use many other gauges and electronic tools that upload information to computer systems to measure the potential amount of snowfall, rainfall etc.
When you go online to websites such as weather.com accuweather.com etc the information that you get on that website is uploaded from those tools that are set out near airports and other regional locations near to where your location is at to give you a weather forecast.
Weather forecast are more accurate now with all the technology but even now weather forecasts can be wrong and any weather forecast over a few days should be taken with a grain of salt.
But I have found most forecasts even a week out to be pretty accurate.