Springtime snowfalls rarely damage emerging plants and, in fact, can protect them with a layer of insulation if severe cold follows. It also presents a perfect photo opportunity, as demonstrated by the snowdrops here.
Late-season snow events should not concern you. The snow generally will not cause any harm and can provide some great photo opportunities. Recently, I admired snowdrops in my garden peeking up out of a light dusting of new snow.
If temperatures drop dramatically after or during the storm, the snow cover will have an insulating effect and help protect the plants from the cold.
Most plants had not grown much before the big snowfall in March since the weather has been cool overall this spring. Plants are more likely to be damaged during springs when there are early periods of warmer-than-normal weather that prompt plants to start growing, followed by severe cold that freezes the new soft growth. In such situations, there is not much you can do other than to cover a few special plants to give some protection against the cold.
A covering of snow on plants is not something you typically need to worry about. However, because late-season snow is often heavy and wet, it is a good idea to carefully remove snow from plants that may be damaged by the weight before it accumulates deeply. Pay closest attention to evergreens, as the snow will more likely build up on them and may bend and damage branches. Arborvitae, in particular, can be bent over to the ground and even partially uprooted in extreme situations.