The first question from one of my friends, after discovering I was pregnant, was, Have you had many nosebleeds yet? And the answer was, All the time. The medical reason I heard was that the nosebleeds are from the extra blood, but I don't think that's the whole story.
The other part of the problem is that we were both pregnant during winter months when it's drier. I took two trips to humid coastal Florida, one in January and one in March, and I didn't have any nosebleeds while there. Also, my friend who was pregnant in Florida didn't get any nosebleeds.
So nosebleeds during pregnancy are common if you're not in a high-humidity environment that helps protect your nasal membranes.