Hello Clark:
Well good luck with the green house, and by all means use the white cedar if you have it available. Many of the historic homes, mills, and barns made good use of this type of wood in particular where dampness was a factor, and strength less of a concern.
Just remember that slightly heavier cross section of sawn pieces may be necessary to beef up load carrying capacities if required.
Of course clear material devoid of knots make for stronger material overall,
Other wood species that fit well into this category of damp rot resistance is hemlock, which is stronger than cedar, and to some extent white oak, which is very strong but suseptible to powder post beetles in damp conditions, and may need some chemical treatment to beef up its resistance.
NH