Thanks, everyone, for the suggestions -- a lot of good ideas to investigate. I'm intrigued by the idea of vitamin deficiency. When I google causes of nosebleeds, vitamin deficiency isn't mentioned, but when I searched vitamin deficiency nosebleeds, lo and behold, I found info on vitamin C and vitamin K deficiencies causing nosebleeds.
My son works in the front end of the grocery store where heat is blowing all the time because of the front doors, and he also spends time outside in the cold, dry air pushing carriages, so I was thinking it was the dry air causing his issues since most of his nosebleeds this winter have been at work (It's not a good thing if your cashier suddenly has a bloody nose!)
Maybe it's actually a vitamin deficiency that is resulting in the dry air causing problems. He has a deviated septum and severe allergies which can contribute to the problem. He had 5 years of allergy shots, which has improved his allergy symptoms, however, he also has oral allergy syndrome. When he eats fruits and vegetables he gets a very itchy throat and swollen, tingly lips. As a result, he pretty much doesn't eat any fruits and vegetables, so he could very well have a vitamin C or K deficiency. He currently takes a multi-vitamin every day, but I think I'll add some additional vitamin C to see if that helps and talk to his doctor about vitamin K at his upcoming appointment.
Thank you, scrubbyfish, for starting this thread!