riding (n.2)
one of the three districts into which Yorkshire was divided, late 13c., from late Old English *þriðing, a relic of Viking rule, from Old Norse ðriðjungr "third part," from ðriði "third" (see third). The initial consonant merged with final consonant of preceding north, west, or east.
riding (n.1)
c.1300, verbal noun from ride (v.). Meaning "teasing, annoying" is from 1927. Riding-hood, worn by women when riding or exposed to weather, is from mid-15c.