Do sea breezes always blow toward beach, like in Corpus? Seems that during a cold front, breezes would blow toward water.
When it is the sea-breeze, it blows landward; when the wind blows offshore as you are referring to, it is called the land-breeze. Thus during most of the year in Texas, the land-breeze blows at night, and the sea-breeze blows during the day. This is because the land is cooler at night, while the sea is cooler during the day.