"The Snow Queen" here being the Anderson's personage. Regina Nix, Regina Nivis, Regina Nivea, Regina Nivosa? Which is closer to the original meaning? (And what is it, at last?) To me, it's not the queen of snow, yet not the snowy queen either. Something in between…
Regina Nix Apposition, although not wrong, isn't the most idiomatic way of saying it.
Regina Nivis sounds better if she rules the snow somehow. We have, of course, Regina caeli 'Queen of Heaven' as a comparison here.
Regina Nivea sounds quite good, although it also has the 'Snowy Queen' feel to it.
Regina Nivosa feels like she is stuffed with snow or fully created of snow.
I will not commit to any translation because it depends on the context.