Yes because fair skin implied that you were rich or upper class. White/pale skin = not working the fields or as a maid cleaning and getting dirty.

That notion got turned on its head relatively recently, when in the 1920 Coco Chanel got a sun tan whilst in the French Rivera. Being tanned no longer meant that you were “low class”.

A lot of old fairy tails are about paths to becoming rich. When Snow White was written it had little to do with race, if anything, and everything to do with classism. There was virtually no social mobility, if you were born poor you stayed poor! These are not aspirational stories designed to motivate you to better yourself, they are there to remind you of your place in the world.