Ok, as a child and even into my teen years, I didn't like to blow my nose either. I would gag, and nearly throw up any time I blew my nose. As I got older, I eventually overcame this, but I always felt that no one understood why I could not blow my nose. I just couldn't stand the gagging and near throwing up each time I tried.
My son, who is 4 1/2, will not blow his nose. I have tried to coax him, teach him, but he refuses. Luckily, he rarely has runny, snotty noses. He does get some crusty stuff in his nose, but he's learned to spray some saline into his nostrils, which loosens what's in there so he can get it out with a tissue, or it makes him sneeze, often sneezing the contents out into a tissue.
With the difficulty I had blowing my nose growing up, I do not feel compelled to force him to blow his nose, as long as it's not creating any major health or hygiene problems.