Only school taxes are frozen. Other taxes and appraisals could increase. Property tax relief would be eaten up in two years by increases in appraisals. Current law caps appraisal increases to a maximum of 10% per year, but lowering the cap to 3% or 5% would keep increases at the inflation rate.
The issue though is that appraisals are a function of the local government, not the State. The local legislature/government would have to put the cap on local property taxes.
CITY and local community college property taxes are ALSO frozen for many senior Texans. The Texas Silver Haired Legislature (TSHL) has been going around Texas pursuing this version of "backyard socialism" for two years. (The kids pay for Grandpa's ambulance, fire, police, senior center, library, roads and other services.) The seniors have plenty of breaks already.
List of Texas towns that have frozen CITY property taxes for seniors and disables (on top of the frozen SCHOOL taxes) http://www.netarrantseniors.net/Freeze%20Status%20in%20Tarrant%20County%20&%20Elsewhere.htm
They are working a petition now to get the voters in Fort Worth to agree to a CITY property tax freeze for seniors. Everybody else's taxes will go up to support this plundering of the public treasury by a special interest group.