I'd wish you luck but, for what it's worth (been a woodworker most of my life) I think you're in for some heartbreak. A couple of factors might effect the outcome to some degree (like whether the oak is quarter sawn or select, etc) but, in all honesty, red oak fares poorly outside. A linseed oil finish is going to last 1 season max due to the fairly extreme movement of oak grain in an outside environment, finsih or no finish. Also, being finished on 1 side will increase the likelihood of cupping/splitting, etc due to moisture exposure on the inside face. You might try sealing both faces. But whatever you do, water's going to get into it eventually and water is not kind to red oak.