Shouts do not consume Magicka, but do undergo varying recharge periods. The longer the duration (hold the button) of the shout, the more powerful the effect and the longer the cooldown period.

Are shouts considered magic?

Shouts are a separate type of Magic from Spells, but cast Voice Power spells at each rank (which are different from "spell spells", like Fireball). Each Voice Power spell applies Magic Effects, which each have their own school (remembering that the first effect defines the spell's school).

Do Skyrim dragons use Magicka?

Of note is that dragons use their Magicka pool for shouts(all dragons have 150 Magicka). If you can manage to keep their pool of Magicka continually depleted through the use of shock spells, they cannot shout at your or anyone else. Dual Casting and Impact help with this.