If you freeze yogurt will the live active cultures still be good?

The live culture in the yogurt does not die when frozen, it becomes dormant instead. After you thaw or eat the yogurt, the dormant culture comes back to life.

The amount of 'live culture' in commercially sold 'frozen yogurt' may only be a fraction of culture compared to regular yogurt. It has to do with the manufacturing process, and not the effect of temperature.

The 'live culture' does die when the yogurt is heated. Heat treated or pasteurized yogurt have no live culture.

I am from India. I always make Dahi (yogurt) at home. I whip and freeze a part of yogurt to start next batch. I thaw out the frozen yogurt in the refrigerator, whip it and use it as a starter for the next batch. When the yogurt is frozen, it does lose the texture. That's is the reason i whip the yogurt before freezing and after thawing.