Many container-grown plants need protection from severe cold if grown in frost-prone areas. The plants that need protection include all tender plants, the not very hardy ones and a number of reasonably hardy plants like rosemary and lavender that may suffer frost damage to the roots if the compost from their containers becomes frozen.
The most effective way to protect these plants and to avoid frost damage is to move them under glass in autumn, before the frost occurs. Tender plants will need some more attention, but the others, depending on the local climate, will do well even in an unheated greenhouse, conservatory or glassed-in porch. The condition is just to keep them almost dry during the coldest, darkest months of winter.
Some of the overwintered plants can be used to provide cuttings in spring and then discarded. If the overwintering space is a problem, then it can be much less space-consuming to overwinter plants as cuttings. Also it worth overwintering under glass cuttings of plants that are not very hardy but are left outdoors over winter. This will provide you an insurance against winter losses.
If your tender plants are too large to be moved indoors you can still protect them from winter cold by wrapping them in insulating material. It is important to insulate plant itself and the container too. The plant can be protected with horticultural fleece or bubble plastic and the container can be covered with straw or hessian and tied snugly around it. This will provide effective insulation for the plant roots and will also protect the container itself from frost damage. Keep these plants in a sheltered place, avoiding frost pockets. Also do not allow heavy accumulations of snow to build up on them as the snow weight can break the plants branches and stems.
In spring, do not rush to take the plants back outside or to let them without any protection. The spring can be often a more difficult season than winter, as there are periods without frost and unseasonably warm days in which plants start their new growths, and these soft, new growths can be devastated by unexpected late frosts if the plants are left unprotected. Also the plants can be damaged by the cold, dry spring winds. Keep the tender plants inside until all risks of late frosts have passed. Plants that have been overwintered under glass will need a hardening-off period of several weeks so that they will be gradually acclimatized to outdoor conditions.
In both cases it is important to remain vigilant and provide protection at night, when there is greatest risk of temperatures falling below freezing. Make sure you keep a sheet of horticultural fleece handy to cover any vulnerable plants if the forecast is for a cold night.