I'm surprised to read this, as twist outs or braids outs leave my hair feeling more moist and soft than plain loose hair. Here's a thought that just popped into my mind. What if it's not a difference in the actual moisture content of your hair, but in how it feels to you? Because braid outs will have lots of bends and kinks in them, they feel less smooth, they feel rougher, than straight hair. So if you compare it to your straight hair it will be less smooth and this is what you are interpreting as dry? Since my hair is very tightly kinked natural, a braid out actually stretches my hair and makes bends and kinks that are bigger and smoother than my natural curl pattern. So to me they feel comparatively soft. How about this idea?
Anyway, I don't do braid outs but usually twist out and I apply a product to my wet or damp hair before twisting. This gives nice results, much better than if i applied product to my hair and left it loose.