Coastal Norway does have its fair share of downfall, though it does vary. The eastern side of the mountains (where this picture is taken) is known for having nice weather most of the year. If you want to see northern Norway in May, be prepared for snow and quite possibly rain. I live in Tromsø and the snow doesn't go away until May/June, but the temperature rarely dips below -5 C. If you stray away from the coast in the arctic, even in June, it might get cold. But southern/eastern Norway in May is often quite nice.
I don't really know how the remaining Nordic countries are in May. I have the feeling western Sweden will be kinda similar to eastern Norway, and that Denmark will feel more spring-like. Regardless, I'm sure you'll find positives even if the weather is shit.