I've read about using the blocks on a patio and how it shouldn't be a problem; however, a portion of my backyard is a remaining slab from a previous house. The previous house was bulldozed, leaving the slab.

I live in Houston, so we rarely freeze.

I imagine the slab is deeper than your regular patio. Do I need to worry about "frost protection" on this slab given my scenario and climate? Is there anything I can check?

Because you are in Houston and probably do not get much frost you should not have any problems. It is doubtful that anything will move from frost. To double check this you can look at old weather records for the coldest month. If the longest period of time for temperatures below freezing is only a couple of days in a row then you have nothing to worry about.

Deckman