Despite her inability to protect herself and not being a warrior, Zelda doesn't hesitate to shoot an enemy full of arrows; she is without a doubt one of the deadliest archers in Hyrule, and had been into archery since she was even younger, and even has given a few pointers to the Gerudos, who plan to get rid of Ganondorf, their fraudulent leader. Regardless if it's horseback archery or archery in general, she can easily snipe anyone without trouble. If any of Ganondorf's men (aka his monsters) or Ganondorf try to touch the ocarina of time or threaten her kingdom, they're met with death or arrow wounds. Princess Zelda may be elegant, cute, adorable, and very fair, but she can strike fear in anyone who tries to harm her, Impa, her father, or Link, regardless if it's a deku scrub or a pesky iron knuckle with only one shot. She can also shoot fire arrows and burn a monster's wooden barricade or shield, freeze bubbles and torch slugs with ice arrows, and has a crossbow inside her bedroom as if she wasn't terrifying enough from a distance.
Ocarina of Time's younger Zelda was in my eyes a fearsome archer in disguise, not just because Impa taught her, but because it's been one of her traits since that god-awful cartoon in the 80s. Adult Princess Zelda can also use a bow, however she prefers to use her sheikah ways to fight as an adult. A gossip stone mentions that she's a tomboy which is true, and she mentions "getting the triforce before ganondorf and killing him" to Link. Also I kinda think she taught Link archery between Ocarina of Time and Majora's Mask since Link can't shoot arrows unless he's adult Link, and in Majora's Mask he can. Lastly she also gives Link the light arrow as an adult which further supports my thoughts.
Ocarina of Time is by Nintendo (c) 1998