Public Utilities

It is unlikely that east-coast strikes would have any significant impact on public utilities, like power and water, in north Texas. It's probable that land-line phones would be unaffected. The only likely exceptions would be if the nuclear strikes are airborne rather than ground-based—AND—they are very large and detonated at a very high altitude. Were that the case, the Texas power grid might be affected to some degree. But again, this is very unlikely.

Internet

As the internet is something of a utility, it is hard to say how local service might be directly affected, or what the federal government might do regarding access to the internet in the US. I'm not aware of any SOPs or expected protocols in such a situation. Local hubs on the east coast would likely be eliminated or damaged, which would have some wider effects. What, precisely, is debatable. At the very least, sites that live on servers in the affected areas and online services that have dependent resources on servers in the affected areas would be down.

Mobile Service

It is likely that mobile service on many/all carriers would be affected nationwide to some degree (and destroyed locally).