Cotton is the source for the vast majority of dress shirtings, but in colder weather a blend of cotton and wool is more practical out of doors and in my opinion has a texture that looks better than pure cotton with tweed.
The first wool and cotton mix was woven by Viyella in England in 1839, and blends are now produced by other makers such as England's Acorn Fabrics. Originally 55% merino wool and 45% cotton in a twill weave, the proportion of wool has over the years declined to 20% to shave cost but it still serves its purpose. Choose from country checks or solids.
Just add wool.