cart (n.)

c. 1200, "two-wheeled vehicle," usually for one horse and often without springs, from Old Norse kartr or a similar Scandinavian source, akin to and replacing Old English cræt "cart, wagon, chariot," perhaps originally "body of a cart made of wickerwork, hamper" and related to Middle Dutch cratte "woven mat, hamper," Dutch krat "basket," Old English cradol (see cradle (n.)).

Many old allusions are from the cart being used to convey offenders to the gallows (and sometimes serving as a drop for hangings) or for public exposure, especially of lewd women, either in the cart or tied to its tail. Compare tumbrel. To put the cart before the horse in a figurative sense "reverse the proper order of things" is from 1510s in those words; the image in other words dates to mid-14c.

cart (v.)

"to carry in a cart," late 14c., from cart (n.). Related: Carted; carting.