Based on your description, the front you are talking about is likely a cold front. A cold front is depicted in weather diagrams with a blue line and triangle symbols pointing in the direction the front is moving, which in your case is toward a warm area represented by red.
When a cold front moves into an area, it typically brings a drop in temperature. The reason is that cold air is denser than warm air, so when the cold front advances, it pushes the warm air upward, often leading to the development of clouds and storms. Since you mentioned that there is a storm moving over the Houston area, this is consistent with the characteristics of a cold front.
As for the pressure system associated with this type of weather, cold fronts are typically found in association with low-pressure systems. Low-pressure systems are associated with rising air, which can lead to cloud formation and precipitation, while high-pressure systems are generally associated with clearer and more stable weather. Therefore, the combination of a cold front and the storm suggests that a low-pressure system is affecting the Houston area.