Cats don't need their whiskers to balance. As in all mammals, a cat's balance is controlled via the inner ear. The myth that cat whiskers affect balance may be related to the fact that cat whiskers are sensory organs. Their function involves distance and space, but not balance.
Balancing Myth and Fact
Lots of animals maintain balance without whiskers, which makes sense because whiskers have nothing to do with balance. All vertebrates share similar balance organs, which developed at the center of the skull long before the evolution of hearing. In mammals, the inner ear—which connects to the middle and external ears—tracks movement and regulates balance.
Whiskers, on the other hand, began evolving 120 million years ago along with early mammals. They're called vibrissae, technically speaking, and most mammals have them. Broadly speaking, vibrissae act as feelers: they are organs of touch.
What Cat Whiskers Actually Do
Most cats have a dozen whiskers on each side of their nose in four horizontal rows—24 total.
Cat whiskers are like radar. Cats use them to gauge distances and size up objects, even in the dark. They help the cat execute graceful, complex movements. Cats also use their whiskers to test the size of openings: their whiskers let them know if they'll fit into tight spaces.
Cats have similar vibrissae on their paws, eyes, chins and legs, but the term "whiskers" generally refers to the ones on their faces.
In addition to their natural functions, your cat's whiskers help you understand him by acting like a mood ring. Are your cat's whiskers at rest? Then he's probably resting too. Are they bunched up and flat against his face? He's being defensive, so he's probably angry or scared. Are they facing forward? That's a sign of curiosity, which means it's time for hunting or play.
Are your cat's whiskers completely forward and on end? Then he's probably startled, but his arched back and poofed-up tail probably already tipped you off.
A Note about Cat Whiskers
Never cut or trim cat whiskers. Your cat's whiskers are a sensory organ, so cutting them off would be just like cutting off your senses of sight, hearing, smell, touch and taste. A cat that loses all his whiskers is usually disoriented and confused. He may even become lost.
Thanks to their tapered shape, cat whiskers are unusually strong and flexible. They grow and are shed naturally. If, through circumstance, whiskers are cut or broken, they'll regrow on their own.