Temperatures below zero can rapidly damage and kill potted plants. Here are a few tip on what to do, and what not to do.
Keeping plants well watered
Surprisingly, wet soil actually allows for increased heat retention, and minimizes frost damage. Moist soil holds heat better than dry soil, and water slowly evaporating around the plant contributes to keeping the plant warm. Adding a layer of mulch can help to enhance this effect. This should be used as a preventive strategy, rather than a response to cold damage where soil is already frozen.
Covering with a blanket or tarp
The cover pictured above is a specialized plant protector for cold conditions. However, if you're not wanting to purchase such an item, you can use tarps, blankets or sheets to provide a certain amount of protection. However, it will be best for the plant if you use stakes to keep the blanket or tarp from touching the foliage.
Don't simple tie it around the stem thinking that the foliage is the only are requiring protection. Wrap your cover around the entire plant.
Don't over-react to damage
If you become aware of frost damage, don't feel you should immediately prune away the damaged areas. Damaged foliage can actually provide protection for those areas of the plant from further damage. Wait until the weather has warmed up before pruning. An exception to this rule is 'soft stemmed' plants, which are more prone to rotting and should be pruned soon after.
Morning sunshine can increase damage
Do not move frozen plants into the sun.
Cold plants in direct sunlight.
Frost damage is more likely to occur as the sun comes up, as the plant defrosts too quickly, damaging leaf and stem cells. Therefore, avoid planting vulnerable species in east facing positions. Lightly misting the leaves of plants before the sun hits them in the morning can also contribute to minimizing rapid defrosting. If possible, move the plants into a position where they do not receive direct morning sunlight.
Plants are generally not forever ruined by frost damage and can be saved. Don't despair at the brown leaves and limp stems, with time and protective responses, most plants will recover. Tolerate those dead leaves until spring comes around, and allow them to provide a protective layer. Keep your plant well fertilized, cover it where possible and don't expose it to morning sunlight where rapid defrosting can occur. Obviously, the ideal response to cold weather is to bring plants indoors over night. However, this obviously an option that is not always feasible.