Brian Cutler emphasizes the importance of cold reading for actors, highlighting that a working actor must be prepared to handle unexpected script changes during auditions. He explains that being asked to read a new script with little to no preparation is common in high-stakes auditions, and the ability to deliver confidently without hesitation leaves a strong impression on casting directors. Cutler advises actors to practice cold reading daily to build the skill and adaptability needed to succeed in these challenging situations.