I can speak for the Romans. Pliny the Elder wrote of mint in his Natural History:

"The very smell of mint reanimates the spirits, and its flavour gives a remarkable zest to food: hence it is that it is so generally an ingredient in our sauces." (20.53)

He lists 41 conditions which mint can be used as a remedy for:

"The juice of mint is good for the voice when a person is about to engage in a contest of eloquence, but only when taken just before. It is employed also with milk as a gargle for swelling of the uvula, with the addition of rue and coriander. With alum, too, it is good for the tonsils of the throat, and, mixed with honey, for roughness of the tongue." (20.53)

Never in his writings on mint does Pliny mention its breath-freshening qualities, so mint was not immediately associated with fresh breath (though the Romans no doubt were aware of the phenomenon, considering it was used for so many oral treatments). Pliny is much more effusive about anise in this capacity:

Pat with bitter-almonds into the cloth strainers for filtering wine, [anise] imparts an agreeable flavour to the wine: it has the effect, also, of sweetening the breath, and removing all bad odours from the mouth, it chewed in the morning with smyrnion and a little honey, the mouth being then rinsed with wine. (20.72)

I'll leave you with this doozy:

"To impart sweetness to the breath, it is recommended to rub the teeth with ashes of burnt mouse-dung and honey: some persons are in the habit of mixing fennel root." (30.9)

I can't speak to how many Romans actually took this advice...