Like many others I'm sensitive to headbob in games, and developers often allow for users to turn the feature off (unlike Bethesda with Fallout 4).
I was looking again today at the remaster trailer and I couldn't help noticing a difference in camera movement between the old and new versions. Old versions = smooth camera. New versions = camera moving slightly up and down. It looks to me like they might have implemented the new camera system from Fallout 4 into the Skyrim Remaster. I seriously hope I'm wrong and they haven't done so.
Have a look at the video and pay attention to the before and after camera movement: https://www.youtube.com/watch?v=GM17Snby-14
(PS: please don't come in just to say that headbob doesn't affect you. That's great but it does affect lots of others)