My impression was that for most trees pruning was mainly done outside the bird breeding season as this was the time when trees were dormant and when it would not affect birds, this was certainly the case years ago from my memory. However the local council here seem to have switched to pruning trees in summer, they are currently (as I type this) removing whole trees or cutting them back significantly and have been for a number of weeks. Presumably they have checked for active birds nests.
When typing this the AI suggested a link to the earlier forum topic on the extensive felling of healthy trees in Sheffield. In the case of the council here they are not felling large numbers of healty trees but are felling or cutting back some species that grow into large trees and doing the usual tactic of replacing them with trees that don’t grow large i.e. that produce much less ‘ecosystem services’.
Certainly, winter-season pruning has been the basis of coppicing/pollarding/layering for many years, in both commercial and conservation circles. It is debatable whether this originally arose out of a belief that the trees survived better if such work was done while they were dormant, or because the people had more time for such work in winter, when other farm/land management work was less demanding.
Practical experience suggests that many species will tolerate/survive summer cutting, but I expect some are more robust than others. Councils (and subcontracted permanent-way maintenance companies) seem to ignore the calendar, and respond to complaints/funding availability rather than practical considerations.
But the more significant impact - particularly on coppiced trees - is probably now Muntjac browsing. Some advocate no coppicing unless the stools can be adequately protected: they may not survive otherwise. There may be some advantage in summer work, as the deer may be able to find other food more readily - but I don’t imagine that influences much of what goes on in the human world!