Not quite.
Texas has two types of registration for 25+ year old vehicles. Antique and Vintage.
Vintage can be used for normal personal use and is also eligible for Year-Of-Manufacture (YOM) plates. You can run the state issued plate with a Model-T on it, or a set of clean, approved plates that were issued the same year as your vehicle. You still have to register it and inspect it every year and you still have two stickers in the front window.
Antique has a rolling five year registration. Depending on when you register it the first time, it might be one month, or 59 months before it will need to be renewed. Renewal is every five years after that. There are no mileage restrictions, but there are activity restrictions as you are only supposed to drive it to events, at events, or for repairs or maintenance. FWIW, a Sunday drive in the country is OK with Texas Sheriffs. There is no periodic safety inspection, but if you bring the car in from out of state, it will have to have an initial inspection to get the green-sheet to get the title transferred to your name, and if you have a gross failure that is obvious to the police, they may cite you for it and require an inspection before renewing the registration. There are two tiny stickers, but they can be put on the rear license plate. The state issues plates for Antique with a Model-T in the center, but you can pay a little more an use your own YOM plates.