@HedaP, if it's a nice day, you may only encounter snow on the ground as you approach Ibaneta--and in that case it's not really that big a deal--it will be packed down and pretty easy to walk on. And it may not even be too chilly. The weather could be shocking, but if you keep and eye on the forecast you could always adjust your departure a day or two to avoid it. So not to overthink or worry too much.
I last went through there in early March 2015 and wore only a fleece, hat, and gloves--and it was fine. The feet got a bit chilly from all the snow and slush, but it was no big deal in the end. The important thing is not to overheat climbing up from Valcarlos--and then end up at the top where it's flat and more exposed/windy in sweaty clammy clothes! This is not the antarctic we're talking about. So no need to start out from Valcarlos all bundled up.
That said. If the weather is shocking and you have no cold tolerance, you may need to stop and put on some more layers of protection.
And know you can easily send excess clothes on to Santiago from Pamplona. You'll see what you need when you get there.
(PS I'm not from a snowy place either--so not to think I'm blase because I grew up stomping in lots of cold white stuff. Far from it--I'm from Hawaii, and later NZ. You'll be right.
)