Place caramels and water in top portion of a double boiler. Heat until melted, stirring occasionally (chopsticks do a good job) until caramel is smooth, about 10 minutes.
While caramels melt, push Popsicle sticks into stem area of the apples. Line a baking sheet with wax paper. Place chopped nuts in a bowl. Let caramel cool for 1 minute (so that it thickens and adheres better to the apples). Dip apples, one at a time, in caramel so that it comes about two-thirds of the way up the apple. Twirl apple as you remove it from caramel. Working quickly, press apple in pistachio nuts, using about 1 tablespoon of nuts per apple. Stand apples, stick-side up, on wax paper. Place apples in refrigerator for 5 minutes to set caramel.
Place a little gold star on the handle end of each Popsicle stick to add a festive touch to this unexpected fun-to-eat treat.
One serving equals 1 apple, 6 caramels, and 1 tablespoon nuts.