As long as it gets done well before buds begin to swell late in winter, the meticulous and specialized pruning that deciduous fruit trees and roses require during winter dormancy does not need to be done immediately. Here where the climate is so mild, some roses may still be blooming. The main advantage to getting an early start is that those of us who have many fruit trees and roses in need of pruning have more time to get them all done within the proper time.
If it helps to start pruning early, it is best to prune fruit trees and roses in the same order that they go dormant and defoliate. The ‘stone’ fruits (those of the genus Prunus, that have large pits known as ‘stones’), like apricots, cherries, nectarines and peaches typically defoliate earlier than the ‘pomme’ fruits, like apples, pears and quinces. Modern ‘carpet’ roses may not defoliate completely, so can be delayed until after all the bare roses get pruned, but may eventually need to get pruned while still partially foliated.
The specialized pruning that deciduous fruit trees and roses need is serious business. Those who do not know how to do it properly should learn about it before actually doing it. Improper pruning of fruit trees can inhibit production and damage the trees. Roses are not so easily damaged, but will get overgrown and not bloom as well if not pruned aggressively enough. (This sort of pruning will be a topic later in the season.)
Like fruit trees and roses, other trees and shrubs that need pruning prefer to be pruned while dormant through autumn and winter. Deciduous trees and shrubs are obviously dormant while bare, but realistically, are ready to be pruned when their foliage is no longer green.
Evergreen plants are not so obviously dormant, but will be as dormant as they get through winter. This would therefore be a good time to prune to eliminate pine limbs that are too low. If pruned a bit early, the pruning wounds will get weathered more through winter and consequently bleed less through spring.