The vee of chest exposed by an overcoat is least protected part of the body to the winter's cold, and the fix for keeping it (and the neck that is found in close proximity) warm is of course to cover the exposed area with another layer of cloth. That layer, usually known as the scarf, is the most important form of neckwear for a man's health and well being as well as an important element of his appearance.
Good guidelines for scarves that complement the day's clothing in my opinion are to pair patterned scarves with solid overcoats or, in the absence of a coat, suits. Solid scarves easily complement patterned overcoats and patterned suits. The pattern or solid should be a different but complementary color.
Color and pattern aside, the choice of scarf material is an, ahem, material consideration. The reason why World War I fighter pilots wore those glamorous silk scarves was to keep their necks unchafed. Silk performs the same function still, as do cashmere and blends of angora and wool. Most plain wool is too harsh, and things like linen and cotton too lightweight for the cold.
New on the ASW store this week are fringed cashmere scarves in four solid secondary colors that will complement most ensembles. They join a dozen other silk, patterned cashmere and lambswool/angora blend scarves in multiple colorways for your consideration.