Petunias, marigolds, zinnia, and other annuals grown in containers will die when frosts get too severe. Most perennials (plant that comes back year after year), however, can be maintained over the winter if steps are taken to protect them. I’m going to refer primarily to trees and shrubs, but the principles apply to any perennial you want to overwinter.
The two primary enemies to a successful overwintering are, 1) Roots getting too cold, 2) Potted soil media drying out. There are secondary issues to watch out for that will also be discussed.
Providing cold protection
First and foremost, you should consider additional cold protection. The more cold hardy the plants, the more likely you are to keep them alive. The USDA zone hardiness of a plant is based on the plant in the ground. Roots in a potted plant are more exposed to the cold than those in the ground. Depending on your perennial, it may be fine wintering in a pot. For example, much of our area is defined as a Zone 5. If your plant is hardy to Zone 3, it will likely survive in a pot with no winter protection. If you plant is listed as a 4 or 5, however, it is more at risk to winter injury/death and would benefit from added protection.
You have some choices for cold protection. First, you can simply dig a hole and bury the pot(s). Alternatively, you can cover the entire pot(s) in straw, leaves, bark mulch, or another similar material. For this method, it helps to first place your pot in a box, larger pot, or wire enclosure to keep the insulating material contained around the pot. Even piling snow up around a pot will offer added protection. A third option is to place the pot in an unheated garage, shed, or basement. Temperature should stay below 40 degrees Fahrenheit. Also avoid swings in the potted soil temperature. This means stay away from the south and southwest sides of structures where reflective heat on a sunny winter day may warm the soil in potted plants. You want to maintain as constant soil temperature as possible.
More sensitive plants (at an equal or higher hardiness Zone) may need additional insulation to the above ground portion of the plant.
Maintaining moist soil
One of the greatest risks to placing potted perennials inside a structure is the potting soil drying out. If you place your pots in an area that is protected from winter precipitation, you must periodically check to ensure moist soil is maintained. Don’t overwater, however, or you may get root rot. Plants that are outdoors typically maintain potted soil moisture unless there are persistent dry conditions. Watering outdoor pots should continue as long as the air temperature is above 40 degrees Fahrenheit. Dry soil will freeze more quickly and get colder than moist soil. Also keep in mind that potted evergreens will require more vigilance in keeping the soil moist as they continue to transpire throughout the winter. Once the soil freezes, don’t water. Ponded water in the pot will freeze and the ice expansion can damage the trunk of trees/shrubs.