Can rosacea on scalp cause hair loss or hair thinning? or do rosacea sufferers have thinner hair?
The diagnosis of rosacea has many forms of severity and symptoms (see here), but it is generally limited to the face, not scalp. Hair loss isn’t a usual side effect of rosacea as far as I’m aware.
I found a post on the National Rosacea Society forum that discusses having scalp inflammation in addition to the facial rosacea, which might be of some help. You should talk to your dermatologist to determine the cause of your hair loss.