Cold reading, especially in Los Angeles, means using your sides as you audition. Actors who are auditioning for lead roles are using their sides all the way through the audition process. If your goal is to become a working actor it’s imperative that you learn to work with the script in hand.
When you audition, casting expects you to use your sides. I often tell my students that being a great cold reader is a separate technical skill that has nothing do with your innate talent. It’s important to get comfortable with the process and you can with practice. Think of integrating the pages into your performance, not just holding them. Working from memory or improving is dangerous. You should be familiar with the material, but also know how to comfortably grab words off the page as needed.