I like plaid neckties made of silk to wear when it is warm. That is because we wear patterned tailored clothing to a greater extent in the fall than we do in spring, when the solid tan gabardines and light gray fresco suits are out of storage. Those latter ensembles benefit from some additional complexity in the accompanying accessories, and, on appropriate occasions (like the Bermudan tobacco break in the Esquire illustration), a colorful plaid necktie can supply it.
For maximum effect it is better that the tie be made of silk or silk and cotton rather than entirely cotton. Just as color is better suited to sunshine, the sheen of silk in a necktie is, in my opinion, more important than it is under the gray skies of winter.
Madras, tartan, or some other style all suit the bill. Wear plaid neckties in summer.