The thinking behind this popular practice is to protect the evergreens from winter sun and drying winter winds. This can sometimes be an important thing to do for young evergreens, especially ones planted late in the season but it should only be done for the first season. Also in many cases its not necessarily the winter wind but the evergreens inability to draw water from the frozen ground. The winter landscape can replicate desert conditions making the plants susceptible to winterburn. Properly watering the evergreens in the fall and all the way up to the ground freezing will help prevent the winterburn from happening.
Another reason many burlap evergreens, especially cedars, is to prevent the winter snow and ice from splitting them as any branches bent by snow and ice will not return to normal in the spring. The best way to prevent that from happening is to wrap the cedars with twine or I prefer fishing line. Its almost invisible, keeps the evergreen tight to prevent the snow from weighing on the branches and allows you to still have winter interest.
Evergreens aside, the one ornamental tree that should be protected with burlap in the winter is the Japanese Maple. The best way to protect this tender tree is to water well into the fall and after its leaves have dropped, put 4 wooden stakes in the ground around the perimeter of the tree and then wrap the stakes with burlap to create a screen. The stakes should be about 1.5' to 2' away from the trunk.
We still want the tree to get the snow cover but want to protect the tree from the winter wind until it is established. This should only be done for the first 2 years until the tree is established. Another case where location matters due to the winter wind patterns. I am still sad that I cannot have a Japanese Maple in my front yard due to its North East exposure. Note I have yews planted instead of cedars for that very same reason.
Simply put, plant the right tree in the right spot, water well into December and use fishing line to wrap evergreens. All my secrets to a burlap free garden!