I walked the first half of the Norte in mid-late April this year, and I do not know why a guide book would tell you its not a good time to walk. All I can think of is weather. The Norte is only a few hours drive from the Francis at all points, but the weather is different.
1) You start and end most days at sea level versus 800m on the Frances, so on average it is warmer in the cooler months
2) You are next to the ocean, so on average it is cooler in the warm months
3) You have the Pyrenees on your left at all times, so that makes for much greater rainfall levels due to orographic effects
All of this played out for us as we walked. It was definitely warmer and wetter than the same time of year on the Frances, but not to any enormous effect. I see no reason not to walk the Norte in Spring, unless swimming at the beaches that you cruise by daily is in the plans. Definitely too cold to swim. As the beaches are the main draw in what is really a tourist area, the number of tourists was negligible, and you could see it in the beach towns. To me, that's a plus for a pilgrim as you are not competing with tourists for beds.
Buen Camino