My take on the move and Texas.
Texas is a helluva large state ... if DFW is your destination I can give little advice except it's hotter than where I live in the woods here in East Texas but I'm 75 miles from the coast and the humidity can be cut with a knife. The closer to the coast the more wet the air is. Get up in the morning in Galveston and there's water dripping off of everything almost like it rained.
More on the coastal thangy. The Gulf of Mexico is brown pretty much all the way to the mid coast (600 miles of coastline from Orange to Brownsville). Not pollution but a plume of sediment from the outflow from the Mississippi River and westward flowing ocean (Gulf) currents. If the water is brown don't expect white sand until south of Rockport (see what I did there RP?). The only advantage I can see is the daily onshore breezes which can be blustery but keep it cooler coming off the water and all. When it's 105 in DFW it's 95 along the coast and 50 miles inland. Did I mention hurricanes? The upper Texas coast has been whacked and flooded 3 times since 2005. I'm talking 70" of rain in 3 days flooded. Even me being 75 miles inland got devastated by Hurricane Rita in 2005 with no power for 3 weeks and heavy timber losses on my lands. In DFW all you have are heat, tornadoes, and hail.
Having said all that we had a wonderful spring from early March until about 10 days ago. Now we are gearing up for sticky summertime ... 2 showers a day and pool, lake, and creek times.
Further from the coast the less humidity and more heat.
I'm happy where I live, if I weren't I'd move. My wife is Canadian and loves it. She never wants to see snow again ... ever !
Anyway ... my take on the Texas weather scene.