Interestingly Haagen-Dazs doesn't mean anything. It's not a Danish maid, snowy days or a dollop of goodness, it's just a term that Mattus, a Polish-American entrepreneur, threw together in 1961 because it sounded foreign and evoked the goodness of a pure dairy product. He even added the umlaut over "a" to make it sound more authentic. So much so, when the brand reached France, they couldn't even pronounce it!
Many Indians might face a similar problem of pronouncing it but like other luxury brands, currently it's the tag conscious that Haagen-Dazs wants to get to its side. Maybe they had the "restricted only to holders of international passports", playing on the Indian mentality of feeling exclusive all the time. Then again, it was not the right time. But Haagen-Dazs knows, "waiting only makes it sweeter".