When the horses have nice thick winter coats, they often do not need blankets. There are plenty of good reasons for blanketing though. As already stated, if the horse doesn't grow a good coat, that is definitely a reason to blanket. A cold horse burns a lot of calories just trying to stay warm.
If the horse's coat gets soaked through with water or mud, their natural insulation can no longer work. We get a lot of rain here and everything turns to mud. During the winter, we are making daily decisions as to whether or not to blanket.
Typically for snow, we don't blanket. The horses LOVE to roll and play in the snow and it doesn't usually soak them to the skin. The older guys always get blanketed first if there is any question whether they may need the extra warmth.