The kanji "kaze" is also used as a suffix...which is huu: method, manner, way, style, -like, looking. So I would take it to mean snow-like ^^; The kanji for blizzard (fubuki as mentioned above) doesn't contain the kanji for wind.
As for the romanization...I believe that most romanization styles don't just translate a double u as a single u, it will usually have a line over it...just like the ou sound will be a o with a line over it.
Hope that helps a little.