I would think that fresh wood chips especially with leaves mixed in from living trees would all be considered green? Just like fresh grass clippings added to any compost is green whereas dried fallen leaves are considered brown because they were already dead when collected. Adding a lot of green (moisture) is what typically causes hot compost where a lot of brown create cold compost which is what you want with a chicken run with deep litter. So adding fresh wood chips even in a hot climate is more likely to create the right conditions for things like mold because of locked in moisture and heat from hot composting. I don't have a lot of experience with it but that is what I garnered from the research I've done on different composting methods.