In my experience both dogwoods and Japanese maples like water more than the average shrub. I think the drought affected them last fall more than was apparent and then after the winter you are seeing the delayed effect of the drought and going into winter without enough water. I would just trim off all the dead branches and make sure they get enough water going forward. I think they will be fine.

I agree 100% with Nancy's comment. Neither tree is the least bit drought tolerant and both species need periodic deep and slow watering during any hot and dry periods.

JM's also experience stem and branch dieback during even mild winters so if branches are still bare now and a bit off color, cut them off cleanly. Be sure to clean pruners after each cut to avoid transmitting any diseases.