I walked those dates last year and started in snow. I agree with both the above comments.
Personally I prefer a jacket to a poncho. I found that the worst thing was the wind, blowing from the left all across the meseta, it was bitterly cold, I saw plenty of torn and discarded ponchos. Actually the wind started well before the meseta, in Pamplona the temperature was -4 but I saw in a newspaper that, with wind chill, it was reckoned to be about -14C. By April last year it was warm and springlike, there's no knowing what it will be like next year though here in Spain the sun can shine at any time and when it does it is effective, remember, when you take off layers you still have to carry them!
It may be because of the vagaries of the weather that you see conflicting info, though, often, people post advice without saying what dates they walked!
Buen camino!
Sue