Call the city sanitation department. In Galveston you pick it up at the recycling center. I think it's the same in Houston.
Tally HO!

If there's such a thing, I'd love to hear about it. I'm skeptical. Houston doesn't seem to give much of a crap about recycling. I could only find one center even remotely close to me for volunteer recyling (since my neighborhood stopping recycling) and it was really gross. It was an independent firm, though. I don't know if there is a city-managed recycling center. I'd love to know about free mulch, but then again I don't have a truck and if it's available it's probably a world away (city sprawl and all).

You probably already found this out but according to the Houston webpage on recycling at:
http://www.houstontx.gov/solidwaste/recycling.html

"During the holiday season there are numerous drop-off sites located around the city. The trees are chipped and converted into mulch products for sale back to the public."

I think we can only assume they do the same for the rest of the recycling garden materials they collect thru out the year. Oh well.