Every time I go to the high desert in CA or NV, especially on my Fall fishing trips, I get this. Not the full cement nose thing, but when I blow my nose in the morning, there's lots of red in the tissue. I wonder if one's body becomes accustomed to that environment after a while, or if everyone just deals with it? Maybe yours is just secreting more mucus to counteract the unaccustomed very low humidity.
I have generally not been a fan of humid environments, but maybe there's something to be said for them. :)