Would people from one kingdom ever change themselves cosmetically to look like someone in another kingdom because they admired their style? For example an Autumnian dyeing their hair to be like a Winterian?

Yes, I definitely think so. Meira even says something like that in SNOW LIKE ASHES, at the beginning of Chapter Three — it’s a flashback where she’s talking to Alysson in Autumn about how she wishes she looked like the Autumnians. I think that’s a natural part of life, admiring beauty in other forms and, more, wanting what you don’t have. 

(Though of course I’d want the way the people in Primoria to go about changing their styles to look like other kingdoms to be respectful and not cultural appropriation…but exploring that topic could turn into another crazy long Tumblr post.)