A description of what we would now call an "old-fashioned" (whiskey, sugar, water, and bitters) is referred to under the name "cocktail" in a newspaper dating back to 1806.

"Always a thing" might be a bit of a stretch, but the history of mixed drinks is very, very old. The idea of adding other ingredients to wine which would change the flavor dates over thousand years in both China and India, although the end result is closer to what we'd think of as aromatized wines like vermouth and was usually done for medicinal purposes. Mulled wine is closer to what you're probably looking for, and dates back to at least the Middle Ages in Europe. The crude nature of early hard liquor made a necessity, and in the 1600's through the early 1800's punch was very popular. Single-serving mixed drinks, of the sort usually made and consumed today, appear to date back to sometime in the 1700's, and overshadowed punches in popularity in the early 19th century.