Yes, I have gas heat going on now and it dries out everything I have!! I put vaseline up my nose because my nose gets scabs inside. I know, gross, but I have to do something about it!
I agree with the others - look into a humidifier.
Another thing to do is keep the heat as low as you can while still being comfortable. That not only reduces the drying of the air but also keeps your heating bills down.
Years ago my wife and I visited her aunt during the middle of a Pennsylvania winter. She kept her house at 74 degrees and after two nights I honestly thought I was going to have to leave and stay somewhere else. I was waking multiple times a night barely able to breathe, the slightest movement of my mouth caused my lips to split, and my skin was dry and scaly. In the end I realised she had another spare bedroom with no radiator in it so I slept in there. It was brutally cold getting into bed in an unheated room in December but I soon learned to cope, at least I could sleep.
It's rare for me to turn the heating higher than about 66.