A twig is a loose impediment and no, may not be moved in a hazard. (I'm sure aaa will correct me if I'm wrong...

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By definition, an obstruction is anything "artificial".
So it might seem that when talking generally to people who are unsure of the rules/processes once they get into a hazard, it is easier to say "you can't move anything" rather than go into the chapter and verse of the almost 200 page publication that is the Rule book.
In an ideal world, you probably wouldn't/shouldn't encounter a moveable obstruction in a hazard on a golf course, but where I play, the odd drink can or snack wrapper finds its way onto the course.
If you can grab a copy of the rule book, or go online to either the R&A or USGA sites you can view links from there I think, Rules 23, 24 & 26 deal with Loose Impediments, Obstructions and Water Hazards respectively and how to proceed should you find yourself in one.
Enjoy your golfing.
Cheers
