Without going back to my advanced physics books, lease don't make pull them out.

Take and object in one hand and hold it a shoulder height with your arm straight out. Now hold the arm with nothing in stright out so that both arms are a shoulder height, one with an object in it. Now drop the object and at the same time pull the arm with nothing in it down as fast as you can. I'll bet the arm with nothing in it can move faster the the object everytime. Oh, you can use whatever arrowdynamic object that you want to.

Now jet compare the fast twitch muscle fiber in a human to a deer, which one do you suppose is faster. I'll let you figure that one out.

Now you mentioned suction cups on a deers feet (they are really called hooves). Now I know that deer do not have suction cups. But, God has supplied them with hooves which really do give them some really good balance and footing (or should I call it hooving LOL). And they can "dig in" when needed. So there is another force acting on them besides gravity (unless deer can fly or are suspended above the ground for some reason), namely the force of their muscles.