mid-12c., "person of ribald speech;" c. 1300, "person fond of chiding abusive language," especially a shrewish woman [Johnson defines the noun as "A clamourous, rude, mean, low, foul-mouthed woman"], from Old Norse skald "poet" (see skald).
The sense evolution might reflect the fact that Germanic poets (like their Celtic counterparts) were famously feared for their ability to lampoon and mock (as in skaldskapr "poetry," also, in Icelandic law books, "libel in verse").
The noun meaning "act of scolding" is by 1726 but seems not to have been in common use. In old law, common scold (Latin communis rixatrix) is from late 15c.
We have not sufficient adjudications to enable us to define this offence with certainty ; but probably a definition substantially correct is the following : A common scold is one, who, by the practice of frequent scolding, disturbs the repose of the neighborhood. [Joel Prentiss Bishop, "Commentaries on the Criminal Law," Boston, 1858]
late 14c., scolden, "be abusive; be quarrelsome," from scold (n.). "Now with milder sense ... To use undignified vehemence or persistence in reproof or fault-finding" [OED]. Transitive sense "chide or find fault with" (someone) is by 1715. Related: Scolded; scolding. Among the many collections of 15th century terms of association appears a skoldenge of kempsters for "a group of wool- or flax-combers."