Yes, unless you "winterize" it by blowing the pipes free of water before the cold sets in. You should research exactly how to do this on a hot tub website like the one below
Hot tub covers can indeed prevent your hot tub from being damaged. they prevent leaves from falling into your hot tub, which can clog up various pipes and whatnot in your hot tub. Also, anything else...
A hot tub is a small pool of hot water, usually bubbling.
WIKIPEDIA states...
A hot tub is a large home-made or manufactured tub or small pool full of heated water and used for soaking,...