It all has to do with the fact that the temperature on the ground is not the same as the temperature up in the air where the precipitation forms.
Snow forms when the air is below 32 from the surface all the way up to the clouds where the snow forms. Snowflakes are collections of ice crystals, and thus need below freezing temperatures to form--and below freezing temperatures to remain snow all the way to the ground.
Freezing rain occurs when snowflakes that have formed in the clouds fall through a warm patch of air before hitting another cold batch of air. That cold batch of air supercools the rain but it hits the ground before refreezing.
That supercooled rain then quickly freezes when it hits ground, trees, power lines or anything else that is at or below freezing.
Significant accumulation of freezing rain that lasts several hours can result in an ice storm.
Another form of winter weather you often hear about is sleet.
Sleet happens when snowflakes fall through a thin layer of warm air. The snowflakes partially melt and then refreeze when they hit another batch of cold air.
That causes the slushy precipitation to refreeze before hitting the ground. That's why you'll see sleet bounce off hard surfaces.