Don't use it green, Suzie. Never use green (freshly-cut) wood in the smoker - way too much moisture and will not make good smoke. Depending on the size of the "twigs" (if less than 1" in diameter, I'd save them for crafts or something), you're going to have to age them for several months, even up to a year, to be good as smoker wood.
If you get some branches, that you can cut into manageable sizes, I'd recommend storing them somewhere in the house, where airflow can get around them (drying racks), not just in a pile. It's a slow process, drawing moisture out of wood, but is certainly worthwhile! If you dry your own wood, you pretty much need to purchase a moisture meter, so you know when it's ready.
I've also heard of people drying wood in the oven, but I'd be a little nervous about the results of that. Could be wrong, though - might be worth some research.
