Since tan is a neutral color, the color of the shirt can be almost any solid or patterned shirt. Even a different shade of tan would work well.
Patterns such as plaids, checks, geometrics, animal prints and retro prints all work with tan corduroys for both men and women.
Depending on the mood, styles can be bold and feature winter brights such as reds, wines, shades of purple, blues, greens and yellows. For a more conservative style, a winter white shirt, pastel pink or light blue work well. One simply cannot go wrong in trying to match a color to tan corduroy pants.