When are you going to be here? Many school districts in the area are on break either the week of 9-13 or 16-20 March (just for awareness- the spots you visit may be a bit busier).
All that you are hearing about layers is spot on. I live near the DFW airport. Last week, it was sunny and I had the windows open; today it is grey and I am wearing sweaters. The weather could be anywhere from 50-80. Depending on where you are coming from, this will likely be a pleasantly warm change.
I moved to DFW from DC about 18 months ago and will give you a little insight into what I have seen and learn since the move. Texans wear a lot more color (the DC palette is often black, grey, and navy); things will be brighter. And shinier- there is a lot of jewelry and general bling; my eight-year-old niece summed this up happily with the mantra "shiny is pretty" (she is a convert). So feel free to pack fewer clothes and accessorize more. There will be boots in Dallas- and even more boots if you head to Fort Worth; the two cities have distinct flavors: Dallas is flashier and oil money; Fort Worth is cattle ranch and Western. Amon Carter (from Fort Worth) said that Dallas is where the East peters out; Fort Worth is where the West begins. Texans tend to dress up more- less frump, more pulled together- it's something to think about when you are going out to dinner or off to a museum. And on the subject of food, DFW has great food. And the Mexican food really is so much better. Order queso and some guacamole made at your table.
As to what to do, you likely have some of that planned out already. I like the Fort Worth Botanic Garden (http://fwbg.org) and have heard great things about the Dallas Arboretum (http://www.dallasarboretum.org). The Dallas Museum of Art is a favorite place of mine (https://www.dma.org). I love the Fort Worth Zoo (https://www.fortworthzoo.org/plan-a-visit/) and given that it is likely to be mild and spring-like during your visit, this could be a great way to spend a day. Dallas has loads of shopping, which may not be of interest to you, as you like have many similar store where you are. But if you want to do some nice shopping and window shopping, North Park Mall has great stores and (this is MY favorite part) instead of kiosks selling iPhone cases and Dead Sea Salt lotion, the public areas in the mall are filled with sculptures and botanic arrangements. Greenville Avenue is very cool- hip restaurants and shops, as is Deep Ellum. And two final favorites near SMU- JD's Chippery (http://www.jdschippery.com) for cookies (get a snicker doodle- trust me; PS- bring cash) and right around the corner- Bubba's for seriously good fried chicken and home cooking (http://bubbasdallas.com). Actually, all of Snider Plaza (http://www.sniderplaza.net) is pretty nice.
Well, that is likely more than you wanted to know. I hope you enjoy your visit. Please let me know if there is anything else you need.