With the possible exception of artillery uniforms, which were generally, but not always, faced in red and the uniforms of riflemen, who most often sported green, I'm not aware of any European tradition for any particular color.
The Regiment of US Dragoons started out in 1833 with yellow as their facing, piping and braid color. In 1840, troopers of the 2d Dragoons breached regulations by wearing a yellow band around their forage caps. With the introduction of the 1851 regulations and the frock coat, the Dragoons went to orange stripes, collars, cuffs, pom poms, and shako trim. Orange was retained as piping and stripes on the 1854 shell jacket as well as for braid on the 1858 Hardee hat. When Dragoons became officially re-designated as Cavalry in August of 1861, they (many of them unwillingly) converted to cavalry yellow. piping on their shell jackets and stripes.
To Join the Company of Military Historians click here