The smallest twig or grass stem can badly deflect an arrow, leading to complete misses on animals or, worse, poorly placed hits. Never try to shoot through obstacles. If you don't have a wide-open shot, do not even consider drawing and aiming your bow.
An animal you can see clearly might present an impossible shot because intervening foliage will deflect your arrow. At midrange, an arrow rises well above your line of sight, which means it could hit overhanging tree limbs above your line of sight at midrange before it reaches the target. Or, because the arrow starts below your line of sight, it could hit super-close limbs before it even rises to your line of sight.
In some cases, an intimate knowledge of arrow trajectory can help you use obstacles to good advantage. I once shot a mule deer by aiming directly through a bush. The bush was 15 yards in front of me, and the buck was 35 yards away. I knew my arrow would sail over the obstruction and arch into the deer. It worked perfectly, and the critter never suspected a thing because I remained hidden during the shot.
Study the trajectory of your arrows before you hunt, and learn to visualize that trajectory from pointblank range to distant targets. If you develop an ability to "think" your arrows all the way to animals, you'll eliminate arrow-deflection problems when you're shooting at game.