There are some warmer caminos that you might consider, where snow won't be a problem, the but in March, rain might be. I have walked both the Levante (from Valencia) and the Via de la Plata (from Sevilla, though you can also walk from Cadiz or Malaga), as have many other forum members, and though you would have one snow possibility in the mountain crossing before Avila on the Levante, the proximity of roads would probably give you a good road alternative if the camino were blocked with snow. The roads aren't heavily travelled, but hopefully the snow would be removed. On the Vdlp, I don't think snow is a problem at all, and there are people walking this route year round, though the killer months of summer are usually not recommended.
Or wait till later. I walked the Lebaniego/Vadiniense in June and it wasn't high summer yet, so May is likely to be on the chilly side in parts.
Buen camino, Laurie