Read the forum guidelines
Can I become a CoxWifi hot-spot using a router running DD-WRT or OpenWRT?
In short, no. You need a Panoramic gateway for that. Why would you want to?
Only if you promise not to peek at our usernames and passwords traversing your personal router.
Not to say you can't make a captive portal. Just not one labeled CoxWifi for reasons Bruce mentioned.
Users aren't monetized for doing that?
No. Cox wants control over their hotspots, so they only put it Cox hardware. Being a "man in the middle" would be a security nightmare.