You could argue the same thing in English here (using a French word). But yes I agree we overuse (and abuse) English words. Don't get me started on the misuse of 's.. <facepalm's/>
Verte chaude would be grammatically correct, though if there's just a dash of Chartreuse in a cup of hot chocolate, I'd wager the gender of the most statically significant beverage should prevail (Vert chaud).
Also chances are you'd drink those from a mug or cup, not a glass.