late 14c., "measured ground for a combat, joust, race., etc.," in a Scottish source, and according to OED "Until the latter part of the 19thy cent. only in Sc. use;" probably from Old French renc, reng "row, line," from Frankish or another Germanic source, from Proto-Germanic *hringaz "something curved, circle" (from PIE root *sker- (2) "to turn, bend"). But probably much confused in meaning with ring (n.1), also used for "area marked out for a sporting contest."
By 1787 (Burns) as "a sheet of ice measured off for curling;" extended to smooth wooden floors for roller-skating by 1875, to ice surfaces measured for ice hockey by 1896. By 1895 as "building containing a skating rink." A modern Latinate word for an ice-skating rink is glaciarium (1876).
Old English is "ice, piece of ice" (also the name of the Anglo-Saxon rune for -i-), from Proto-Germanic *is- "ice" (source also of Old Norse iss, Old Frisian is, Dutch ijs, German Eis), of uncertain origin; possible relatives are Avestan aexa- "frost, ice," isu- "frosty, icy;" Afghan asai "frost." Slang meaning "diamonds" is attested from 1906.
Modern spelling begins to appear 15c. and makes the word look French. On ice "kept out of the way until wanted" is from 1890. Thin ice in the figurative sense is from 1884. To break the ice "to make the first opening to any attempt" is from 1580s, metaphoric of making passages for boats by breaking up river ice though in modern use it usually has implications of "cold reserve." Ice-fishing is from 1869; ice-scraper is from 1789 in cookery.