In order for a winter storm to develop you have to have three basic ingredients.
First you have to have below-freezing temperatures in the clouds and near the ground to make snow and/or ice.
Next is lift to raise up the moist air to form the clouds and cause precipitation. With this lift the warm air is colliding with cold air and being forced to rise over the cold dome, creating a boundary known as a "front" where the clouds will develop.
Finally you have to have moisture that can be lifted to form the clouds and precipitation.
Once all three of these components come together a winter storm has been created.