Options for keeping dog hair out of a pc "tower"?

I have a Labrador retriever who sleeps in my room, and was wondering if anyone has dealt with the potential problem of having dog hairs getting caught in their cooling fans and/or other PC parts.

Would an air filter fan help? Or maybe little meshes that cover each individual cooling fan?

I don't have a complete PC at the moment (buying a few parts at a time) but when the time comes and my build is complete, I would like to put whatever advice you guys have for me to use.