I'm not sure what would be odd about it. Why would horror be any less suited to discussion of literary criticism than any other genre? There was an entire module on Gothic Literature people could do on my English Lit degree (sadly couldn't take it due to scheduling conflict) which covered Frankenstein and Dracula among other works.
Generic critcisim can definitely be applied to how the genre emerged, historical criticism absolutely in how horror works reflect the anxieties of the times they're written in (ie. Dracula and the themes of xenophobia, Frankenstein and worries about scientific hubris), you could absolutely do a Marxist reading of many horror works (in Frankenstein, the Monster just wants the same things humans feel entitled to; shelter and love and he is denied this by his upper-class creator who abandoned responsibility for the monster he unleashed on the world), or a feminist reading (Women as victims... the way virgins often survive while "impure" women with sexual desires and history tend to be killed), or Post-modernist (horror monsters in the popular consciousness and depictions of them divorced from the meaning of their works etc.) And don't even get me started on Queer theory and how vampire stories both celebrate and demonise queer identities.
So yeah, you can definitely explore Literary Theory and Criticism through Horror works, just like any other texts. Horror can actually be a great place for it because it's often such a showcase of "what people are afraid of or anxious about" and how they give that form through metaphor.