1. Fill a shallow basin or dish with ice water and set aside. Line a baking sheet with parchment and set aside. Remove the stems of the apples, and insert the sticks into the tops of the apples. (Alternatively, you can choose to leave the stems on, tie string to the stems, and lower them into caramel.)
2. In a small saucepan over medium-high heat, combine the dairy-free half-and-half, the soy yogurt, sugar and corn syrup, stirring well to dissolve the sugar. Using a candy thermometer, cook the mixture for about 10 minutes without stirring, or until the caramel reaches 245 F. Stir in the soy margarine, mixing until completely melted and incorporated.
3. Remove the pan from the heat and place directly in the ice water. Working quickly, dip each of the apples into the caramel, using a spoon or knife to help coat all of the sides. Transfer the apples to the prepared baking sheet and place in the refrigerator for 20-30 minutes or until set.