Unlike other parts of the U.S., there are few warnings in the White Mountain National Forest about closed roads or inclement weather. Even if a road seems to be maintained, it might only be plowed for the first few hundred feet, to allow snowmobile access. Locals carry chains, collapsable shovels, salt, use studded snow tires, and even weigh down the vehicle with sandbags. I live in California, where there are official "chain-up" areas and such. Don't expect such organization in NH, thank heavens!! But, do use caution entering smaller roads, and don't be foolishly brave.
Drive! And take back roads because they are very scenic. I recommend the Kancamagus Highway (route 112) if you are travelling from the east or west. A lovely winding 2-lane road through the White Mountains with breathtaking scenery and plenty of rest areas where you can stop and enjoy the view. When you get to route 93, head north to Franconia.