I walked late March last year. Just missed Napoleon Route which opened April 1st. I didn't stop for the night at Valcarlos so walked to Roncesvalles from SJPDP on my first day. I wouldn't recommend it - you'll get stronger after a week or so but that was a hard first day for me and I had trained a lot. Late snow last year so cold, wet, muddy, snowy at top of the climb at Roncesvalles. If weather is bad or foggy you can take the road for the last, steepest, maybe coldest bit. If there's still snow on the ground it will be pretty cool in the shade. It was warm around midday in the open. It also got warmer once I headed down towards Zubiri. I don't know if there's a long range weather forecast for this year. First few days can be cool mornings, lots of shade in the forest/valley up towards Roncesvalles, take gloves and a scarf. Don't get dehydrated - easy to do even if it's cool. You'll get used to proper hydration later on but it will be easy to get that wrong on those first days. Do a last minute weather check at the pilgrim office at SJPDP and get a map so you get off the main road ASAP just after SJPDP. Last year, some people got into trouble in foggy weather on the last bit of the climb up towards Roncesvalles. So check into the pilgrim office the morning you leave for an update.
From Pamplona on, you'll be cruising.
Buen Camino, - Mike
Edit: After a few days walking if you find you need some extra key bits of gear try Caminoteca in Pamplona.