It appears The Legend of Zelda: Breath of the Wild uses an upgraded version of Nintendo's classic Mii character creator to design many of its NPCs.
Within Breath of the Wild's files, NPCs are referred to as "UMii"s (Ultimate Miis?), who use a combination of familiar Mii facial components for their various designs.
Breath of the Wild's versions of these components are more detailed, and stylised to fit the game's art style. But it is noticeable how many NPC characters share various bits and pieces of the same face parts.
This also means that, with a bit of code injection, it is possible to customise the game's UMii characters to display with different face pieces, and even get your own Mii in Breath of the Wild too, as HEYimHeroic shows:
"UMiis have almost all the same parameters as Wii U/3DS Miis, with a few minor differences here and there, like moles no longer being supported," HEYimHeroic reported. Some hairstyles are also not included, with Breath of the Wild instead converting outliers into a list of more Zelda-friendly designs.
UMiis represent the bulk of the game's NPCs from both human and hylian races - alas, there's no way to turn yourself into a goron.
You also can't use this method to edit the designs of main characters, whose character models have been created individually - so you'll just have to stick to dressing up or undressing Link as standard.