Each draw is preceded by the procession of the teams onto the ice, led by Pipers playing "Scotland The Brave", "Marie's Wedding", and the like. The sponsor mascot, a large fluffy ball of cotton, also participates. The pictures here give a feel for what goes on. (And note that a curling event has some pretty spectacular optics, the white of the ice, mixed with the colours painted on the ice, the colours in the arena, the colours of the uniforms, etc. It's a great show.)
But I wonder whether the same sort of thing is done in Scotland, where the cultural references here suggest it all originated. Often emigrant communities keep rituals alive long after the homes they left have abandoned them.