St Nicholas is traditionally shown dressed as a Roman Catholic Bishop - mainly in a purple 'cope' (cape) as being both the colour for a bishop and for the Church period leading up to Christmas known as "Advent". I have never associated red (or white) with him, nor seen any references to it in Christian books.
As "Sinta Klaas" (I think), he was imported to the USA and has spread around the world.
Other countries had "Father Winter" who became the same as the English "Father Christmas". They traditionally wore long robes of fur-trimmed green and 'crowns' of holly - as symbols of the re-birth of the year to come.
As they all mixed in together, they created the "Santa Claus" of today.
But he was, in fact, 'finished' by Coca-Cola in the 1920s, when they launched an ad campaign showing the familiar "jolly fat man in the red suit" (trimmed in white).
Red and white were never part of St Nick's 'required colours'.
If you see a well done movie version of "The Christmas Carol", almost always either the "Ghost of Christmas Past" or the "Ghost of Christmas Present" - or both - will appear dressed as Father Christmas/Father Winter, NOT 'Santa Claus' in red and white!