Some may be shocked about the weather possibilities for the next week or so. But when looking at this forecast, always remember that someone else (further north, of course) has it worse off than you do.
A fast subtropical jet stream across northern Mexico into the Texas Gulf Coast will provide energy which, at times, may set off generally light rainfall. This is an Arctic air mass in control of the Lone Star State, so clouds in daytime will make for an awfully chilly feeling. With a gusty north wind and cloud cover, however, nocturnal lows will likely not (locally) get below freezing). Further north and west of Houston, some cases of sleet or freezing drizzle are possible. The threat for frozen precipitation is probably greatest on Wednesday night and Thursday morning. At that point the coldest temperature profiles (with an upper level low) will be making a fairly close pass to the Bayou City.
While at least two important Arctic air masses proceed through the Midwest and Northeast (the second will be truly bitter cold, around January 22 - 24), Texas will be only side-swiped by the frigid domains. Frost and freeze possibilities will loom at night, but daytime readings should have no trouble reaching the 50s and 60s (F). This is all supposing the storm track across the eastern Pacific Ocean does not make us a target, which could indeed be the case.
Someone else has it worse off than you do. Except New England, of course....
Monday: Mostly cloudy, breezy and chilly. A few periods of rain or drizzle may occur. Highs 48 Madisonville to 52 Bayou Vista
Monday Night: Cloudy, breezy and chilly. Lows 37 Huntsville to 41 Hitchcock
Tuesday: Cloudy, breezy and chilly with drizzle. Highs 46 New Waverly to 50 Santa Fe
Tuesday Night: Cloudy, breezy and chilly with drizzle. Some freezing drizzle and sleet possible north of FM 1488 and TX 242. Lows 33 Willis to 37 Alvin
Wednesday: Mostly cloudy and cold. Highs 43 Bentwater to 47 Arcola
Thursday: Sunny and cold. High 49, Low 28
Friday: Sunny and cool. High 55, Low 31
Saturday: Sunny and milder. High 61, Low 36