I walked in May, a month later, where you would think would be warmer. I had days I was comfortable, as long as the sun was out, which did not seem to be often. Many more days where I was soooo cold. That wind!
At the Arco de Caparra, I had long johns with pants, two pairs socks, 4 top layers and ended up putting my poncho on to break the wind. I used my sarong to wrap my head and neck. That wind was so strong it sliced that cold into me. In June I woke up to see snow on the mountains. The locals were complaining of the crazy weather Spain is having.
Now mind you, I am from a warm weather place so I have a different tolerance than northerners, but the French group that was also there were huddling to keep warm. So yeah, prepare for all climes.
I loved the Via.... have fun
Lillian