From the Colorado DOW below. I guess you can harvest as many as you like. Personally I will advoid them but will watch them. One that we saw looked like a 5 foot aligator with a shell, dont believe Id like to catch that. If I catch a glimpse of that one again I will try to take a picture.
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Snapping Turtle
Season: Statewide, from April 1 through October 31.
Daily bag & possession limit: Unlimited.
License and manner of take: Snapping turtles may be taken by anyone in possession of a
valid Colorado fishing license or small game hunting license, and by any method not
specifically prohibited by regulation or law.