Depends, I don't use bark when I cold smoke but for longer cooks it doesn't matter to me. I can't tell the difference. I don't use chips I use chunks so it would probably depend on what type is smoker as well.
Personally, I wouldn't use green wood to smoke with. It needs to be seasoned first. If it's just small limbs, I doubt cherry wood from a fruit tree would have enough bark on it to worry about removing.
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