Am I Weird?

[*winter*]

I just sent an unsolicited résumé and (embarrassing got long) cover letter to a person in a position of power in an organization I'd love to work for.

So...is it weird to send a résumé when the org isn't actively hiring on its website?

And...how long should a cover letter be? Mine was actually four pages. Which I know is incredibly long but I had a lot to say... And it's like my dream job.