I started HRT this year (Femoston Conti) and when I started with these headaches this Summer I blamed the tablets and nearly gave up. My doctor was really good and suggested that the headaches might be due to the pollen count being high (I'd only taken a couple of tablets at the time). I spent the entire Summer monitoring the pollen count and right enough, when it was high I had a headache.
I'm not an expert on antihistamines but I think the older ones that make you drowsy are the worst for drying you out. I take Loratadine when I need to. Didn't help much with the headaches mind you.
I have noticed with the menopause generally though that everything is dry (dry enough to be a nuisance) - nose, sinuses, itchy ears, eyelids, VA etc etc. I'm trying to get used it all and find a way of managing :-)