To ensure that your popsicles have a creamy texture without becoming icy, consider using ingredients that have a higher fat content. Incorporating ingredients like cream, whole milk, or even yogurt can help maintain a smooth and creamy consistency. Additionally, using natural thickeners such as cornstarch or gelatin can prevent the formation of ice crystals and create a richer texture. Freezing the popsicles at the right temperature and for the appropriate duration is also essential in preventing iciness.