Fellow Houstonian homebrewer here.
I have tried the tub 'n' towel, and ice, and fan, etc. The humidity in Houston is just too high to make the evaporative cooler work sufficiently - unless, you keep your house AC in the mid-60s. We had one of the hottest and dryest Junes on record this year, and the towel only brought temps down by about 6 degrees F.
If you have the time and attention to manage with a tub of water and ice, then that would probably work - I did not have the time. I reached a point where my freezer couldn't make ice fast enough to keep up, and so I resorted to buying ice - just brings up the cost per pour (for me, to commercial beer prices, and my beer still tasted terrible).
I was ONLY able to get fermentation temperatures under control by picking up a scratch-and-dent chest freezer from Lowe's and controlling temperatures in it with a temperature controller. I have brewed 17 batches in all, at this point - only the last three were temperature controlled in the chest freezer, and the last three are actually good, FINALLY!!
TL:DR: all previous repliers are 100% correct in writing that fermentation temperature is paramount, but all folks this deep in the country's armpit that I've talked with use a fridge or freezer - folks about the Great Lakes and New England and the Rockies just don't get it.
Get a refrigerator or chest freezer and a temperature controller.