The recent cut backs at the zoo resulted in cutting some of the days when the zoo is free.  Here is the current list of holidays the Houston Zoo is open free to the public:

Columbus Day
Friday after Thanksgiving
New Years Day
MLK Day
President’s Day  
 
Specials Exhibits

The special exhibit that they have from time to time aren't free for holiday visitors. You better be prepared to spend a few bucks, if you want your kids want to see the exhibits or these favorites.

Educational programs
The train
Lecture series
Ticketed special events 

The holiday hours at the zoo are 9 a.m.- 6 p.m. get there early,  in case the place gets overcrowded and they have to shutoff admissions.
  
Houston Zoo Free For SNAPS  Recipients

If your family receives SNAPS via the Lone Star Card, you are able to visit the Houston Zoo anyday during the year for free.

Here’s what you need to have with you:

A current award letter from SNAPS( Texas food stamp program)
A photo ID (Texas Drivers License or Texas Department of Public Safety photo ID card)

Only 5 persons per visit (2 adults/3 children) and the Lone Star Card holder must accompany their party.

How To Apply For Free Admission With SNAPS Award

Present a valid  award letter along with a photo ID of the card holder at the ticket booth to receive zoo tickets.

You can't pick-up tickets in advance, only on the day of you visit the zoo visit. Free admission to the Houston Zoo is  limited  to viewing the regular zoo attractions and does not apply to any ticketed exhibits.  

However, there is no limit on the number of times you can bring your family to  the zoo using a SNAPS award letter.

Looking for more information on attractions in Houston, visit Midtownlive.