We mostly buried our containers with
perennial shrubs in the ground with the plan to pile up the snow.
It is better that perennial plant soil is moist as the freezing of the soil helps to insulate the
roots compared to dry soil when frozen provide not much insulation. I also piled some dead branches around my perennial shrubs to trap the snow. The thicker the snow over the plants and the longer we can keep snow in the late winter the better especially if you have plants that might be less tolerant of the cold winters.
Some people will take out their dormant plants from the container and heed them (bury) into the ground for the winter and put them back in their pots in the springtime when they are still dormant.
Another possible solution is the put
straw bales around your container and make sure that the snow is piled around the pot and above. (But the ground is always the best) Some will put their pots in an unheated garage that keeps just below freezing all winter.