I built a screened in room on my deck in the rear of my house. The "roof" is plastic sheeting supported by 1x4s, nominally but really 3/4"x 3 1/2"s of wood. It has an 8' clear span and it hasn't sagged in 7 yrs of Pa. winters with a foot or more of snow on it. If you can, I would use a 1x3(true dimensions).
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