Clematis vine and cling by using their leaf petioles so they need a relatively thin membered structure as a support. They will not attach well to a cedar fence, although if the vine is advanced enough (tall) you can train it to just drape over the fence and it will grow along the top surface.

But a trellis really works best....or a tree or shrub it can clamber through

Clematis wants to twine around something about the thickness of a pencil. A metal trellis will work.