Yes, drain pipes freeze in Texas, but rarely, and almost always in an exposed spot rather than underground. Drains hold little standing water and empty after each use. The exceptions are traps and short runs in cold places: an outdoor kitchen sink, a garage or pool bath, an attic condensate line.
The main sewer line is the least likely part to freeze. North Texas residential code amendments, as adopted by cities such as Murphy, list a frost line depth of 6 inches, and sewer lines are usually buried deeper than that. Ice in a sewer line points to a section that runs exposed, such as a cleanout riser or a pipe in a pier and beam crawlspace.
The trap is the usual weak point. Each sink, tub and floor drain holds water in its trap to block sewer gas, and a trap in an outside wall, crawlspace or outdoor cabinet can freeze in a hard cold snap. So can a condensate line in a cold attic, or a cold trap fed by an all-night drip. The sign is a fixture that will not drain after a freeze, then works once it warms up. A sewer smell can come with it, as the guide on what to do if your pipes freeze notes.
Thaw a frozen trap gently with a hair dryer on low or warm towels. Skip boiling water, which can soften plastic joints, and chemical drain cleaner, which just sits on the ice. In an empty, unheated house, shut off the water and pour nontoxic RV antifreeze, never car antifreeze, into each trap. One honest limit: a drain that stays blocked after the thaw is not frozen. It is a clog or a cracked trap, and it needs drain cleaning or a repair.