As a general rule, no. Just like drought dormancy, very little water is required. And unlike drought dormancy, it's simply not being lost in any great amount. Dormant grasses won't require more than a quarter of an inch of rainfall per month, maximum. That's about the recommended amount of watering to maintain life in KBG during summer dormancy, it'd be overkill during winter, but certainly not damaging.

Very long-term dryness during winter dormancy might want a bit of moisture, but that's not usually an issue. Evaporation is near-zero in cold weather--effectively zero at freezing or below, although sublimation of ice is certainly not zero in any weather, particularly sunny weather, no matter how cold.

Transpiration is effectively zero from winter-dormant grass, so we can call the usage of water zero. Even the roots aren't using more than the most-minor amounts to break down sugars into carbon dioxide and energy.

James is in Houston if I recall correctly.

Part of this has to do with rainfall. We Texans typically get enough rain in the winter so that we do not have to irrigate. Beyond that, I believe the answer is more about the soil than the plants. In my part of Texas we have a few plants that remain green all winter. Some of those are grasses and continue to grow all winter. In fact I kinda need to mow next weekend. But even for the parts of the yard with no growing grass, I believe it is important to keep the soil hydrated periodically. The microbes inhabiting the soil might not be active but they are alive. Allowing them to become desiccated can kill them.

This is supposed to be an el Nino year, so I'm absolutely counting on getting plenty of rain all winter. This past weekend was just the first pass of el Nino events. We got 2.25 inches of much needed rain in my gauge. I believe Houston got a lot more than we did.