I started on the 6 March in Pamplona, as I was told that the Pyrenees might be to risky to cross because of the snow.
Throughout the whole of March I had perfect walking conditions with only 2 or 3 days of rain. Most of the time I walked in t-shirts, but of course you will need a jacket and a fleeze for the mornings. Also the big advantage is that it's not so crowded, I never had any problems to get a bed in the albergues. I had a light-weight sleeping bag (750gr) with me, for the really cold nights you always can ask the hospitalero for a blanket.
When I crossed the Cebreiro it was sunny and warm, though 3 days later I saw on the Spanish TV that it was snowing again and Pilgrims walking through the snow, so you never really know and you will need to be prepared.
After all, I still believe that March is the best month for the Camino, not so crowded and not too hot, and the best of all - you walk into the spring!