I was driving down south last week when I noticed some seriously butchered crape myrtles along 395 in a prominent location along the highway. I don't want to embarrass anyone so I've included pictures from outside the area of this common offense to plant physiology.
There are a couple problems with this practice often given the grim moniker of crape murder. It's not as common in the Owens Valley as other places, but there is no reason why we need to catch up with the rest of the world in this case.
Second, crape myrtles are marginally hardy in Owens Valley. At least the above ground parts. When the limbs are topped, I've noticed dieback from freezing from the early new growth that emerges in spring. That leaves a stub with some weird branches that grow about 12” from the big cut.
Early spring, not winter, seems to be our most damaging season to crape myrtles. I don't have any real data on this, but my experience here and in Arkansas is that fall pruned crape myrtles are more likely to have winter damage in extreme years or late winters. Probably makes no difference in mild climates.
For the most part crape myrtles need no pruning. They are actually an easy plant. Easy is good! If you'd like a neater looking bush, you can clip the spent flower parts off and thin out some small branches to improve the shape. If you do need to make a major cut, in this area it's best to wait until the new growth begins in spring. They are usually slow to start here so be patient.
If one of the big limbs starts to look terrible or dies over winter, go ahead and remove the whole thing. It will be replaced with a new shoot in late spring.
Finally, it's OK to prune plants, but try to have a real reason. I can't think of any reason to top crape myrtles. It's not needed at all. They are naturally a graceful plant.