The short answer is "it depends." You could have rain and / or snow every day, or dry clear skies. It is impossible to know until you arrive. So, follow the advice of others who recommend you "bring the full kit."
Plan on wearing layers that you can add to or strip off as the case may be. If, along the way, you determine that packing extra layers is asinine or redundant, you can always ship it ahead using the Correos, to Ivar at Casa Ivar in Santiago. He will gladly hold it for you.
I have experienced ankle-deep snow on the Napoleon Pass over the Pyrenees during the last week of April. Then, I have also experienced wet snow three times at Cruz de Ferro, several weeks on in my Caminos - each time in Mid-May. I have also go caught in a white out, short but furious, at O Cebriero in early May.
In this circumstance, I advise bringing a fleece mid-garment (I like a zip up front), an ultra-fleece "beanie" watch cap, and gloves. Also, wearing a rucksack poncho improves your ability to wear layers, and keep your rucksack dry as well.
Also, you should always have one or two "Buffs" anyway. They can be used for a wide variety of expedient uses, including wearing around your neck for warmth - or soaked in water and worn around your neck and wrists in hot sun for a type of expedient air conditioning.
Hope this helps.
Tom