Are there any sites free from snow in Norway in March? I'm planning an bicycle tour in Norway,so I want to ride bike safely.
The entire southern part of the west coast (let's say at least from Stavanger to Kristiansund) is so mild in the winter, that there is usually very little snow there. Ålesund had for example last winter only two days entirely below 0°C. Really cold weather usually only comes together with clear weather, so the combination of freezing temperatures and precipitation as snow is very rare.
The coast of Rogaland (around Stavanger-Haugesund) and Møre og Romsdal (around Ålesund-Kristiansund) is relatively dry with little precipitation at all in the late winter or early spring.
It won't be warm, and you are of course not guaranteed to avoid snow, but chances are indeed high that it will be relatively dry and snow-free in these regions.
Looking at Accuweather for last March, it looks like the weather will be mostly cold-ish, from +6c to -5c pretty much everywhere in Southern Norway ( I looked at Bergen, Kristiansand and Olso).
It can get colder and it can get hotter, it is still winter and there will be snow, there surely will be cold rain on the coast.
If you are not used to ride in cold/rain/snow I would not advise doing it.