to win something hands down (1855) is from horse racing, from a jockey's gesture of letting the reins go loose in an easy victory.
The Two Thousand Guinea Stakes was not the best contested one that it has been our fortune to assist at. ... [T]hey were won by Meteor, with Scott for his rider; who went by the post with his hands down, the easiest of all easy half-lengths. Wiseacre certainly did the best in his power to spoil his position, and Misdeal was at one time a little vexatious. [The Sportsman, report from April 26, 1840]
Ancient Greek had akoniti "without a struggle, easily," from akonitos (adj.), literally "without dust," specifically "without the dust of the arena."
"a tidal river," 1650s; see salt (n. ) + river. as a proper name, it was used early 19c. with reference to backwoods inhabitants of the U.S., especially those of Kentucky (there is a Salt River in the Bluegrass region of the state; the river is not salty, but salt manufactured from salt licks in the area was shipped down the river). The U.S. political slang phrase to row (someone) up Salt River "send (someone) to political defeat" probably owes its origin to this geographical reference, as the first attested use (1828) is in a Kentucky context. The phrase may also refer to the salt of tears.