Basically, yes. Your garden will always recover but it will take some time and for sure some work. At first you should cut back all the broken branches. To avoid holes in hedges or trees you might have to cut them back completely. Also, overexpanded branches which do not get back into the shape they had before should be trimmed. If you have overexpanded young trees which do not straighten up you have to tie them to a pale for 2 - 3 years. With this support, the tree can keep itself upright. By the way, it was good that you didn´t act directly on this phenomenon because you wouldn't have had good chances to get the ice off.