Purslane is a Portulaca also. Its' species name is oleracea.
You can save it by protecting it from frost, bringing inside in your location.
Taking a perennial plant to where it can't survive perennially does not make it an annual, but they are sold that way to avoid confusion. Many, if not most plants sold as annuals in temperate climates are just not hardy where sold & are really perennials that can be saved if one has that interest. Many of them make great "houseplants."
In the specific case of your moss roses, put next to your most sunny window & water when dry. May stop blooming over winter but should resume again when you are able to take back outside next spring/summer.
