I am wondering if I need to wrap in burlap my boxwood – mountain green – over the winter.
Also Korean dwarf lilac and Japanese cotoneaster.
Also, should I position them together and in a protected area. I have a large wrap around balcony. One side faces west and other side north. Thank YOU
The short answer is that everything you are suggesting will be helpful to your container shrubs over the winter.
Evergreen and deciduous shrubs have three main enemies in the winter: cold temperatures, wind and sun. Alone, but especially together, these cause dessication of the foliage. Anything that can be done to mitigate these factors will help to protect your container plants. Burlap is a great option for wrapping your pots, and there are other similar shelters available. As you suggest, grouping them together in the most sheltered area of your balcony is also recommended.
A rule of thumb for plants that can be grown and overwintered in containers successfully is that they should be hardy to fully two zones colder than our Toronto zone 6, i.e., plants should be hardy to zone 4 or lower to have the strongest chance of survival over the winter. The more winter-hardy the plant, the less vulnerable it will be to the freeze/thaw cycle in containers which happens when temperatures fluctuate rapidly, damaging the plant’s root system.
Your “Green Mountain” boxwood is considered hardy to zone 5a, so it will benefit from some additional protection over winter. The Korean Dwarf Lilac is considered hardy to zone 3a. I am not sure which Cotoneaster you may be referring to as Japanese Cotoneaster. If your plant is Cotoneaster lucidus, sometimes referred to as hedge cotoneaster or Peking cotoneaster, it will be hardy to Zone 2a and should be fine in very cold conditions in a container. However, most of the other varieties of Cotoneaster available are hardy only to zones 5a-6a. These varieties will be more vulnerable, so it would be useful to know the Latin name of the Cotoneaster you have, and protect it accordingly.
The Brooklyn Botanical Garden has an informative article on this subject: https://www.bbg.org/gardening/article/overwintering_potted_plants .
All the best in overwintering your lovely shrubs.