In Texas, nothing is "to far," to a Texan.
I don't personally think there is a lot to do in Dallas, but that is, again, a personal observation. Also, Dallas can get down right cold, with inclement weather.
If you are looking for a few good weeks, consider a 300 mile jaunt down to San Antonio. There is tons of stuff to do in that area. Just the Alamo, and the River Walk, is worth the trip.
There are several CG's in the area, but we stay at Braunig Lake RV Resort on 37S just outside the 410 loop. It is Passport America, and if you are a PA member it would be about $129 for a week, including taxes. Plenty of activities at the CG. The hosts, and people, are really gracious. We may be heading that way if I can get my coach out of service for warranty work. Seems like it has been in there for an eternity.
Braunig is about 7-10 miles from downtown San Antonio.
Austin is nice, but still a little colder than SA. It is about 225 miles South of Dallas, same route to take to get to SA. If you go to Austin, Oak Forest RV Park is nice, but PA is only good for 1 week a year, accumulative, when you use it. Braunig is all the time.
Houston is about 250 miles S of Dallas and I'm about 40 miles South of Houston. We are having a cold spell.
Right now at 10:00 a.m. it is 50 degrees. Plenty of CG's in the area. Some pricey, some not.
Darn! Seems like all the warm places are 250-300 miles South of where you will be.
Edited: Also, around the New Braunfels area there are several campgrounds which puts you within 50 miles of day touring San Antonio, Austin, and other points of interest.
Oh! And we don't refer to you as "Snow Birds," we consider you "Winter Texans."