Plants in containers have a limited volume of soil to protect and insulate their root balls. Also, the potting mix in a container freezes sooner than the soil in a garden bed, since it's surrounded by cold air on all sides.
Fortunately there are a few things you can do to keep your container trees and shrubs safe from winter damage.
If possible, move your containers to a spot sheltered from harsh winds. A south facing wall is a perfect place, since the wall absorbs the sun's heat during the day and radiates it later, when temperatures drop.
You can add insulation outside the pot to make up for the reduced soil insulation inside the pot. Wind a few layers of bubble wrap around a round pot, or tape pieces of styrofoam board insulation to the walls of a rectangular container. Is it beautiful? No. Does it work? Yes! And if you really can't stand to look at the naked insulation, you can cover the bubble wrap or styrofoam board with burlap for a uniform, finished look.
Evergreen trees and shrubs (both broadleaf and needle) need even more assistance from the container gardener. Evergreens hold onto their foliage year round and winter winds wick moisture out of their needles and leaves. If the ground is frozen, plants can't replace the water they lose. As a result, needles and leaves turn brown; this is called dessication.
Broadleaf evergreens (e.g. rhododendrons, hollies, mountain laurel, etc.) are most severely affected. Spray their leaves with an anti-dessicant in late fall to create a vapor barrier that slows the loss of water from the leaves. Anti-dessicants should be reapplied after a heavy rain. They are available at garden centers and nurseries.
If you're not prepared to reapply an anti-dessicant (and you must reapply for this to be effective), you can screen trees or shrubs with burlap. Burlap is breathable enough to allow for air circulation and also offers physical protection from drying winds. But don't tightly wrap the foliage of your evergreens. This keeps all light and air from the foliage. Instead, either construct a screen around your protected holding area, or staple the burlap to three or four stakes places at intervals around the circumference of the pot.
If the temperature gets above 45 degrees on a winter day, your evergreens will start to photosynthesize. Water is released as a byproduct of photosynthesis, and if that water isn't replaced, you're in for some dessicated foliage. Have you ever seen your rhododendrons make it through the winter looking great, only to have the foliage turn brown in late February or early March? These plants warmed up just enough on a sunny afternoon to start photosynthesizing, and they quickly exhausted the moisture available to them. (Remember, the containers are small, and the irrigation system is turned off.) Then, the soil re-froze, the water wasn't replaced, and the leaves were left high and dry. Literally.
Water your container evergreens on a warm winter day and they'll thank you by staying nice and green.