> Does anyone know if a thyroid disorder can have any effect on
> facial hair, i.e. increasing it? or is it just to do with
> hormonal imbalance only?

Since no-one's answered this, yes, thyroid disortders can in some instances be responsible for (or point to the existence of) the hormonal disturbances that lead to incresased hair growth.

If you're looking for information you could look at
http://www.aafp.org/afp/20030615/2565.html
for a start. Or do a Google search on thyroid hirsutism

In a nutshell, the circumstances in which you might look for thyroid involvement would be if you have irregular periods but on the other hand don't have any signs of virilization (Acne, enlarged Clitoris, Deepening of voice, Increased libido, Increased muscle mass (primarily shoulder girdle), Loss of breast tissue or normal female body contour, Malodorous perspiration ).

The article at
http://www.aafp.org/afp/20030615/2565.html
is actaully not at all bad on the subject of hirsutism -- worth a careful read.

Interestingly it makes the point that shaving is the easiest and safest method of hair removal.