Technically they don't have to, but copper does a great job of insulating the mule cocktail to keep it extra cold and frosty. Plus, they are very aesthetically pleasing.u003cbr/u003eu003cbr/u003eThere are a few stories as to how copper mugs became associated with mule cocktails, including that u003ca href=u0022https://www.myrecipes.com/how-to/cooking-questions/why-are-moscow-mules-served-in-copper-mugsu0022 target=u0022_blanku0022 rel=u0022noreferrer noopeneru0022u003ethe copper enhances the flavors. And, another story is that a copper-making company needed to unload a ton of copper mugs and came up with this gimmicku003c/au003e.u003cbr/u003eu003cbr/u003eIf you don't have a copper mug, you can use au003ca href=u0022https://amzn.to/3UiRdZou0022 target=u0022_blanku0022 rel=u0022noreferrer noopener nofollowu0022u003e double old fashioned glassu003c/au003e.