The thought that green wood shrinking around screws will give strength, is based upon using green wood with dry wood, like a green seat shrinking around the dry legs of a chair, something that was done by the rural chair makers. This doesn't much apply to metal fasteners, and actually works in reverse, because the wood will shrink away from the screw head, and become loosened. I guess you could tighten them up from time to time, but shrinking around the shank of the screw won't gain any more strength, compared to a properly sized pre-drilled hole in seasoned wood, being the size of the screw shank into what is being screwed into. The holes in the uprights should be large enough so that the screw slips through with little resistance, and no slop.
I think it would be better to dry the uprights, a durable species as suggested, keeping it out of the hot sun and dry winds. Have extras so that you can toss the ones that don't make it through drying without splitting so bad. Dry slow to reduce splitting, that being out of the wind if possible, and keep them off the ground where air can circulate. Cut them considerably longer than necessary, and trim to length from both ends after the drying. You should be able to trim off the splits. Some species split a lot worse than others. Wood that dimension will dry pretty quickly anyway, unless it's some super dense species.
Green wood does drill easier without splitting, but with dry wood, using a sharp drill bit, and some precautions against splitting, like not being too close to the ends, you will be OK, then lubricate the screws with wax or soap, before driving them home.
Slapping on a coat of exterior preservative every year or so, with an anti-fungal ingredient, should give a good lifetime. Even with dry wood, you might want to go around and tighten the screws from time to time. The change in seasons will loosen up the fasteners.
My 2. Have fun!