I would like to put my roof sheathing on vertical instead of horizontal. It will be an 18 by 12 patio. Rafters are 2 x 6; 16 in on center. It will be 1/2" in plywood which will be visible from below
If it is plywood you are using, it will be difficult to nail into by hand. The plywood is more stable across the joists rather than with the joists. When you run the plywood with the joists and try to nail into it between rafters the plywood will give so much the nails will hardly take if you are driving them by hand. I would not do it this way. It sounds like you are doing this to minimize the exposed joints. This should be a minor concern compared all the nails poking through as mentioned before. A layer of decorative material down first, like T-111 or something similar, then your plywood, will give the underside a nice look without a great cost, and if you gauge your nail length, there will be no nail points popping through.
If you use OSB, the direction you lay that material does not matter, it is structurally stable in either direction. But then you will have nail points all over the place still on the underside.
You can, but horizontal is better since they will cross more rafters, enabling better straddling and distribution of joints, minimizing cupping at the butt-joints, and will have less linear feet of joints sharing rafters (24' vs. 36')