Unless the tree has really sharp bark, they should be ok. I did exactly that, and they were fine.
Great quality shirt. Vented back and pits. Good quality material. One of my complaints is the height of the sleeve rolled up. I'm not a buff dude, but when the sleeves are rolled up, they sit right in the middle of my bicep. Minor inconvenience and you can kind of adjust it so that it is a little more comfy. Second thing is how tight the buttons are. It is tough to do one handed - like when you are rolling your sleeves up. Just 2 minor things. A great shirt, very comfortable.