late 13c., "covering of woven cloth or leather for the lower part of the leg, with or without feet," from late Old English hosa "covering for the leg," from Proto-Germanic *huson- (source also of Old Saxon, Old Norse hosa "covering for the leg between the knee and ankle," Middle High German hose "covering for the leg," German Hose "trousers," Danish hose "hose, stockings;" Middle Dutch hose, Dutch hoos "hose, stocking," also "spout, waterspout"), literally "covering," from PIE root *(s)keu- "to cover, conceal." Old French hose, Old Spanish huesa, Italian uosa are of Germanic origin.
From mid-15c. as "close-fitting garment resembling tights worn by men and boys."
The hose of the middle ages generally covered the person from the waist to the toes; they were secured to the upper garment by points or some similar device. At times the covering of one leg and side of the body was of different material and color from that of the other side. In the sixteenth century the leg-coverings were divided into two parts, and the word hose was applied rather to the breeches, the covering of the lower part of the leg and foot being called the stocking or nether-stock. [Century Dictionary]
Used in Middle English of various things resembling a stocking, such as the sheath or husk of an ear of grain; sense of "flexible rubber tube for conveying liquid" is first attested mid-14c.
c. 1300, "to furnish with stockings," from hose (n.). Meaning "to drench in water as from a hose" is from 1883. Related: Hosed; hosing.