DFW likely gets the front close to midday with rain going to snow during the early afternoon and lasting through the evening though amounts look to be light. I am thinking a dusting to localized couple inches with the most on the east side of DFW.
For the Tyler area I expect the front early afternoon with rain changing to sleet/freezing rain by late afternoon and to snow by evening lasting into Tuesday morning maybe. Areas between I-20 and I -30 in E TX could see 1-3". In Deep E TX I think the front comes through during the evening Monday with rain going to freezing rain and sleet by late evening and changing to snow by Tuesday morning, down here snow will likely be less than an inch but icing could be an issue. For northern SE TX and the Brazos Valley I would give a similar forecast. I do think there is potential that models are currently underestimating moisture return so amounts are more likely to increase than decrease over eastern TX.
I am not a good source for Central Texas, but you could likely extrapolate my above forecasts to include areas of Central Texas.
In short, yes I do think that the front will arrive earlier and a tad colder than forecast. Also moisture could end up deeper than modeled.