You could term the forecast for the next few days as being in the "bit of a chill" category. But nothing worse. In a winter that computer models have continually botched with predictions of longer-term cold intrusions and precipitation events, the following two weeks will prove to be no exception. The current runs of the numerical forecast models have backed away from the idea of excessive cold, and in large part are quite dry for Texas through March 14.
The north breeze which sets up on Wednesday through Friday will drive local temperatures well below normal through Saturday. But keep in mind that seasonal averages are rising, so a prediction of cold will not have as much impact as it would have a month ago (thank our low latitude and increasing sun angle). In any event, a disturbance moving out of the Rocky Mountains should create a warming wind shift on Sunday. It is doubtful that we will see any meaningful rainfall in association with the passage of the cold front associated with the storm on Monday, when highest readings may reach into the 70s and 80s over much of Texas.
Wednesday: Partly sunny, breezy and mild. Highs 62 Madisonville to 66 Galveston
Wednesday Night: Clear, breezy and chilly. Lows 38 Huntsville to 42 Port Bolivar
Thursday: Sunny and cool. Highs 56 New Waverly to 60 Gilchrist
Thursday Night: Clear, breezy and cold. Lows 35 Willis to 39 Caplen
Friday: Variable cloudiness and chilly. Highs 54 Lake Conroe to 58 Crystal Beach
Saturday: Sunny and cool. High 59, Low 37
Sunday: Mostly sunny and milder. High 67, Low 41
Monday: Increasing cloudiness, windy and milder. High 73, Low 49