That paper towel around the drink thing doesn't seem that much faster. Doesn't it take about 15 minutes anyways?
Other ways to quick cool drinks.
1. Spin the drinks in ice water. You don't need the salt and at hotels(at least in the US) ice is abundant. You'll get from room temp to tasty cold in about 2 minutes.
2. Place the drink where the cold air comes out in the freezer. Leave the freezer and fridge door open for about a minute then close. This will kick on the fridge and you get the super cold air to blow on your drink.