I think Picasso made great use of Texture

Picasso's - Goat’s Skull on the Table

Texture is used to describe either the way a three-dimensional work actually feels when touched, or the visual “feel” of a two-dimensional work these qualities are reached through use of color, line, shape, etc. The texture of a logo can be real or simulated. In the three-dimensional world logos can be given texture on signage, clothes, badges, etc. But in the two-dimension/digital world, texture has to be implied. In other words, the design looks like it would feel a certain way.

For more Texture in art check out these sites;

Below are some logos using textures;

For some more info on texture as an element of design
check out of these sites: