It depend what cyclamen and what just how freezing your weather gets in Texas.
In the UK we grow a houseplant cyclamen that is C. persicum and is not frost hardy. This needs to be indoors in winter.
In our gardens we grow a few cyclamen of which C. hederifolium and C. coum are hardy down to about -15C for short periods of time. There are other cyclamen with varying degrees of hardiness between these extremes.
If the cyclamen is hardy in your area it does not need to be covered in freezing weather.

No I have a few in my garden that have been there for years, if they are hardy and meant for outside then they should be alright