Can you install cedar tongue and groove directly to wall studs?

Of course! Horizontal or diagonal installations will work. Just be aware that depending on where the studs are on center, some warping may occur. Depends on environment, quality and thickness of the product, too. I lined the inside of my exterior laundry room with diagonal 1x6 cedar tongue and groove (after insulating w/fiberglass batts). After a couple of years, some small shrinkage and warping, but nothing significant.

Looks awesome!