I agree. The Doe is snorting to ask, " Who's There?" If you snort back- just put your hand over your mouth to send the sound in a slightly different direction, and snort- you are telling her its okay, you are just grazing like she is. Most times she will simply go back to doing what she was doing before the encounter.
Deer don't have good depth perception. Their eyes are on the sides of their heads, to catch movement, but they can't really use their eyes like you do to estimate how far away something is, or often what it is. Their genes tell them that when in doubt. RUN AWAY! When that doe goes running off, snorting, she is saying " I am scared!" to anyone and everyone in the woods.
If you start cussing, or coughing, or talking, and moving around, IT will be YOU who tells the rest of the deer in the woods where you are, what you are, and that you are the one that scared her. Then, they will also avoid you, and the area you are in.
So, take Swamp Rat's suggestion, and simply give a snort back to the doe. At the very worst, it will send her on her way quicker, and at the best, you will experience what I have, and what he has on several occasions.
Another thing to consider taking to your stand is a squirrel bark call. Sometimes, simply making a bark like a squirrel will also calm the deer so you don't give away your position. Obviously this works better when squirrels are active during the day, but deer don't keep track of squirrel's time tables either. I have seen more than one deer spooked by a silly squirrel running and jumping to a tree trunk. And I have seen and heard squirrels barking at deer from the safety of trunks and limbs.