Fall and Spring are best. There are a few good winter walls. Summer only if you hate yourself. I’ve camped in the established campground near Mt Scott and another near a reservoir. Names escape me but both were fine.
Winter is a fine time to visit, there isn't too much of a particular season. Fall and spring are best. Note that the winds in oklahoma can be absolutely heinous and shut down a day.
Reserve camping ahead of time. It can get a bit full, but there's a major campground in the park itself.
In the winter, lost dome and crab eyes are the two areas with the highest density of sunny rock. Mt. Scott has less sun, but also dense. The narrows arent THAT narrow but you certainly will have a but less time in the sun