You can get larger bags of these for cheaper at Tractor Supply or another farm store. They're sold as horse stall bedding. I'm not sure what kind of wood it is either.
I'm new to chickens, but I'm in a hot climate and have read that the breeds with feathered legs like Brahmas and Marans are less heat-tolerant. I have no personal experience with them though.
I'm jealous! My neighbor has a huge mulberry tree that hangs over my yard. I was excited to try the berries, but the birds have already eaten all of them.
I'm going to try propogating my own from a branch...I'll make sure to cover it with bird netting when I do.