Green’s Dictionary of Slang

(US) any cocktail made with crushed ice.

1832		Polit. Examiner 16 June 3/3: In order to moderate the intense heat of mid-day and early afternoon, recourse ought to be had to his Hail-Storms, which infallibly overcome the most sultry drought [DA].
1840		T. Haliburton Clockmaker III 26: Fellers [...] who spend the night in a back room of a market tavern with the key turned, drinkin’ hail-storm and bad rum.
1857		Santa Barbara Gazette 29 Jan. 4/3: The drinks ain’t no good here—there ain’t no variety in them, neither: no white-nose, apple-jack, [...] railroad, hailstorm [DA].