If they are total leafless then look at the base of the plants where the stems enter the soil.  It isn’t unheard of to have mice or rabbits strip the bark off burning bush to eat over winter…especially this last harsher than normal winter.  If you see that the bark is all stripped off then you might as well cut the burning bush right to the ground.  The roots are still fine and the plants will grow back very quickly.  You may even see shoots already emerging from the root system below.  Don’t cut them off since they are the start of the regrowing process.