Green wood won't work. It'll impart resinous flavours, and as it's still fairly wet you'll find any smoke it does give off won't take. And if a chainsaw has been used they'll almost certainly be contaminated with chain oil.
For cold smoking these days, I use a stainless steel pellet burner similar to this one -
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Pellets can be had pretty cheaply, in a variety of wood types (apple, beech, hickory, etc)
I spent long enough trying various methods, and this has proven to be both the easiest and most convenient method for me