Texas did have a problem last year when the freeze happened. It wasn't a serious problem, just one had to go off line.
Navy reactors are very different in design of course, each carrier has two, and the submarines have one of a specific design for them. Those are the only ships (and boats) in the USN with nuclear power today. Carriers need it to save room for aviation fuel (and to enable high speed operations when needed, as in launching).
The main problems with nuclear are expense, which could be managed if we had any sense, and waste, which could be managed if we had any sense.
The two new nuclear reactors at Vogtle are way over budget and way over time.