Or does the snow protect them from the cold?
Should Snow Be Removed From Shrubs During Freezing Weather?
It depends on the type of shrub and how much of a snow load it's carrying.
If the shrub is bent by the weight of snow to "an uncomfortable" angle for an extended time, some shrubs may not be able to recover their shape. A snow load does act as insulation against temperatures (to a degree) and wind, which often does more harm than temperatures.
I find this a difficult question to answer because there are many factors to consider: Is the shrub bent to the breaking point? Is more snow expected before existing snow can melt? How flexible is the plant? Is it safe to be out removing snow?
I have been quilty of making the excuse of getting snow off shrubs to get out of the house and playing in it, only to find broken stems and minor branches from beeing too enthusastic in snow removal. Over the years, I have found a happy medium by gently taking some of the snow load off shrubs that I felt were being weighed down too much, but leaving enough to be of some insulation use.