Why does shaving dehydrate the skin? Is there an hormonal effect involved?
First of all 'Testosterone' hormone controls the growth of hair on our body and also oil secretion. Depending up on the nature of a person's body, this hormone controls the growth of the hair.

Why shaving facial hair leaves the skin dry ?

First let me explain the reason behind the oiliness of the skin. Sebum is produced by the sebaceous glands and is a complex made up of cholesterol, free fatty acids, glycerides, squalene, and wax esters. Sebum and sweat, along with the epidermal lipids discussed earlier, make up the oil on the surface of the skin. Some people will have more oily skin and some have less which depends on the nature of body.

While shaving the sharp razor cuts the hair and also damages the skin and hair follicles. The level of damage to skin also depends whether you are shaving downwards or upwards. Because upward shaving usually causes more damage to skin and hair follicle. Complete detail of damage to hair follicle can be found in this article: Science of shaving.

Shaving also removes skin lipids and water content creates pores which exposes the skin. If the surrounding atmosphere is dry then skin loses water. Or if the surrounding is moist or humid then water content will be balanced. That is the reason why we use artificial face moisturizer for immediate remedy to avoid infection and balance the wetness of face. So it takes a while for the skin to get back to normal state if nothing is done after shaving which sometime leads to acne or rashes due to infection.

Another reason for dry face is use of hot water which removes skin oil instantaneously. So lukewarm water or cold water will further reduce the dryness of the skin. (Use of shaving cream with high alkaline content will obviously result in dry skin. This holds for soaps also.)

Complete details can be found in the first link provided and Drying skin after shave.