Finally, a TradGang topic that I know something about! I spent seventeen years training and working with SAR dogs. Avalanche dogs will frequently locate a person under the snow from the victim's exhalations. I've had dogs dig to the face numerous times, favoring it over the feet end of a person. These exhalations are one of the reasons that SAR dogs have not been fooled by "scent-blocking" clothing in tests. (There are other reasons that I won't discuss here.)
The odor of your breath starts with the exhalation of warm, moist air from your lungs. It passes up through your trachea, mouth and/or nose. All along the way, it carries with it cast-off cells that are in a perfect environment -- warm and moist -- to feed the microbes that produce odoriferous gases. Deer and other critters can easily distinguish these odors as originating from something "strange" and therefore potentially dangerous. (SAR dogs are easily trained to distinguish human scent from all other scent sources.)
Your breath also conveys the odor of gases from microbial action on the stuff that is in your stomach from your meal(s) and in your bloodstream. Eating strongly-scented stuff that doesn't occur naturally in the deer's environment is therefore not good practice. I stay away from such foods during deer season for that reason. I am sufficiently impressed with the reasoning behind the meatless approach that I'm considering testing it this year. (Fairly easy for me, since I live with a vegetarian.)
You can reduce the gas production "somewhat" with the chlorophyll. You can limit the distribution of exhaled cells and warm, moist breath "somewhat" by covering your mouth and nose. "Somewhat" is not "all together," which is why being downwind is still a very good idea.