Welcome to the forum
@Cesnouf and Buen Camino!
Immediately you get to St Jean Pied de Port go to the Pilgrims Office at 39 Rue de la Citadelle in the old part of town, up the hill towards the ramparts. It is pretty easy to find - St Jean is a small town.
The Pilgrims Office is
the place to get information on the weather, the route conditions, and available accommodation. You can also pick up a credential if you do not have one, get your first stamp, and meet up with other pilgrims.
It sounds like the weather is very cold at the moment but as the Route Napoleon does not open until the end of March, you will be walking through Valcarlos anyway. Probably have to stick to the road - there is a track that runs beside the road and dips in and out of the beach forest, but it would be dangerous in snow or heavy rain.
Take a luminous mesh safety vest! They are really lightweight, and although the traffic on the road is light there are spots where the road is narrow and you need to be visible. A safety vest could be a lifesaver. I'd also stick some of the luminous tape on my backpack.