Grooming and cleaning your dog's nose is a very important part of taking care of your dog. If you allow a lot of hair to grow around his nose, it could find its way into the inside of his nostrils. This can lead to irritation and a wide range of medical issues that have a chance to become chronic.
On top of this, if your dog has allergies or a cold (yes, your dog can catch a cold) or anything else that can lead to nasal discharge, you need to keep his nose clean and well-groomed to prevent bacteria from being able to enter his body via his nose.
From your dog's perspective, the constant tickling or itching resulting from long nose hair can be enough to drive him crazy. You may see him constantly rubbing his face on the furniture or carpet, or endlessly licking his nose. Your dog does not want to have to go through like this, it is your job to make sure he doesn't have to.
Your dog needs his nose to always be in tip-top operating condition. It is his guide to virtually anything he wants or anywhere he wants to go. It is up to you to keep hair trimmed back and any discharge cleaned up. If you are gentle enough, your pup will actually look forward to this when he has a cold. Take your time, be gentle, and stick to it, a clean nose is an essential part of your dog's overall health.