As a caveat to the forecast which follows: there continues to be a problem with data loss from rawinsonde stations in the Pacific Ocean theater. Since coverage of this vast area is sparse to begin with. The lack of usable wind and temperature information invariably hurts the accuracy of numerical models that use the observations. Bottom line is that the predictions based on those schemes may or may not be very viable. But here goes!
As it turns out, the colder air in the Midwest and Northeast will never touch Houston, and may only get into the northeastern part of Texas on Friday night and Saturday. The Bayou City will stay mild with considerable night/morning fog into the weekend. Showers may work into the picture Sunday and Monday in conjunction with a fresh breeze off of the Gulf of Mexico.
A surge of Arctic air with a full latitude trough will approach on Tuesday. A wave of low pressure forming on this boundary may set off heavy rain and thunderstorms. Later next week this feature could turn into a big snow, ice and wind machine over parts of the Mid-South and Appalachia, with the bitter cold air streaking southward from Canada. For Texas, the "big chill" arrives Wednesday morning and likely will stay through the following weekend. I also cannot rule out a storm affecting the western Gulf Coast around February 4 - 5.
Friday: Partly sunny and mild following dense morning fog. Highs 76 The Woodlands to 80 La Marque
Friday Night: Partly cloudy with dense fog developing. Lows 56 Spring to 60 Webster
Saturday: Dense morning fog; partly cloudy and breezy by afternoon. A shower is possible. Highs 73 Tomball to 77 Dickinson
Saturday Night: Partly cloudy, breezy and mild. Lows 60 Klein to 64 Seabrook
Sunday: Variable cloudiness, breezy and mild with a few showers. Highs 75 Cypress to 79 South Houston
Monday: Variable cloudiness, windy, warm and humid with a few showers. High 80, Low 62
Tuesday: Variable cloudiness, windy and mild with showers. Heavy thunderstorms are likely late day and at night. High 77, Low 63
Wednesday: Morning showers; then cloudy windy and much colder. High 70 (A.M.), Low 42 (P.M.)