My son is five years old. He has been in the pool since he was ten months old. He is not afraid of the water, but he cannot learn to keep his mouth closed and blow out his nose.
I understand your concerns, but we are supposed to use our mouths to breathe in and out during swimming, not our noses.
If your son is swimming along with his mouth wide open, taking in gallons of water, then yes, this is a problem. He should be swimming with his mouth closed unless he needs to inhale.
The reason we use our mouth to breathe during swimming is the simple fact that the opening of our mouth is larger than our nose, and therefore, we can get more air in and out in a shorter time than we can through our nose.
Teach your son to blow bubbles on the water's surface. Get some toys to blow along and turn it into a game. Kids always learn fast when whatever they are doing is fun and enjoyable. Egg flips are great fun and a great learning tool. They are designed to flip over and change colour when they are blown.
Gradually, breathing in and out through the mouth will become second nature to your son, and he will develop a natural breathing technique ready for when he starts to learn the four basic swimming strokes.
In the meantime, make sure whatever you do in the water with him it is fun. Use plenty of toys that float and sink to that he can also learn how to hold his breath and submerge. That is, of course, if he is not already doing that!
I hope you find this advice helpful, and I wish you and your son every success with your swimming.