To Show Submission
Another reason dogs sometimes covers their faces or noses is to show deference to their pack leader. Hiding their face could be a sign that your dog trusts you and wants you to know they're not a threat. If this is the reason for covering their face, they may also follow the behavior by rolling over to expose their belly.
To Please You
While dogs don't have a concept of cuteness as you understand it, they're highly perceptive and can tell when their behavior pleases you. Since dogs are often eager to please, they're likely to repeat something that they know amuses you. In other words, when your dog covers their face they might simply be trying to make you smile.
Should You Discourage a Dog From Hiding Their Face?

Face covering isn't seen as a negative behavior and there's no reason to discourage it, says Wag! That said, if face hiding is caused by pain, itching, anxiety or fear, the behavior should stop, or at least lessen, once the source of the behavior is taken care of.
A dog hiding their face is usually a form of communication. As a dog parent, it's important to pay attention to what your pup is trying to tell you. Check in with your dog to make sure they're okay before reaching for the camera to catch the cuteness in action.