For my own interpretation, which I have been working on for quite a few years, I see the dress and coat looking a little like Winter Fantasy™ Barbie® (2003), which I have on my shelf.
I like the idea of a shimmering dress and a white fur trimmed coat. For the belt buckle, I plan on using a metallic snow flake Christmas decoration type thing, which I can starting November in many different sores. As for the tiara, I would like something a little more "ice" like. For example, I really like this Swarovski Cristal tiara:Swarovski Cristal Tiara
Hair wise, I had thought of getting custom made dreads in white, blond, silver and maybe light blue, to look like icicles; unfortunately, my favourite dread maker, Elliss Seven of LS Seven Hair, no longer takes custom orders, so I'm no longer sure exactly what I'll do. We'll see.
As for makeup, I have shimmering white powder which I can use on the top part of my face, shimmering turquoise powder I would use as eye shadow and blush, and silver lipstick for an icy look.
The Snow Queen by Hans Christian Andersen has been one of my favourite stories since childhood. I could make a whole wardrobe for my Snow Queen if I didn't hold myself back.