Unfortunately its not just that easy. You should always attempt to get the botanical name of any plant you purchase or otherwise obtain. You may not have an interest in those names but it certainly helps when you need to look them up or ask a question about them.
Ice Plant is the common name of about 5 different plants so I'm not sure what you have. However it will probably freeze and die regardless. It needs to be treated as an annual here in San Antonio.

The Copper plant (Acalypha wildesiana) is an annual and will freeze and die.
Pentas (Pentas lanceolata) are tropical perennials and will freeze to the ground and probably die with the first freeze or frost. In a very mild winter they might come back from the roots.
Mexican bird-of-paradise (Caesalpinia mexicana) and the bird-of-paradise which may be either (Caesalpinia gillesii) or (Caesalpinia pulcherrima) are perennials that will probably freeze to the ground and return from their roots. They should be mulched heavily for winter protection.

Sago palm (Cycas revoluta), while normally root-hardy here will suffer freeze or frost damage to its foliage. Protection such as a large cardboard box or blanket should be provided when temperatures below 32 degrees are forecast.
Bougainvillea is a tropical perennial which might survive a freeze if planted in a protected location and mulched heavily. However, they do not do well in San Antonio planted in the ground and it is recommended that they be container grown. Then they can be brought into a protected location when freezing weather comes.
Texas Star Hibiscus (Hibiscus coccineus) is a root-hardy perennial that will freeze to the ground and return from its roots.
Mexican firebush (which I am going to assume is Hamelia patens) is a root-hardy perennial that will freeze to the ground and usually return from its roots. Mulching will help this one to survive.
Dwarf plumbago (Ceratostigma plumbaginoides) is a hardy perennial that will freeze to the ground and return from its roots.