Would the Karstarks be considered a princely house prior to the Conquest? House Stark of Karl's Hold was founded by one of the son's of a King of Winter, so he must have been a prince, and logically his descendants must have been as well. I don't believe there are any references to it in the text, and it seems bizarre to me that a house so distantly related to the main branch would retain the title of "prince" (the ASOIAF wiki tells me says the house was founded "a thousand years ago"). At the same time, it seems odd to me that they'd officially change their name to "Karstark" if they derived their princely status from being related to the main branch of House Stark; and it's not like at one point they would have gone "I'm X+1 generations away from Karlon Stark, so I guess I can't inherit the title of 'prince' from my father".
Were the Karstarks princes and princesses while the Starks were kings, right up until Aegon's conquest, or did they no longer hold those titles by then?