At the end of April, the Napoleon Pass is officially open , but might be closed due to snow. The Pilgrim Office at SJPdP has the official current status.
Be aware that it is possible to have some snow all along the
Camino Frances, at elevations of about 700 meters ASL through the end of May. This also means that nighttime and early morning temperatures can be in the single digits celsius until the sun warms things up.
I have personally had snow at Cruz de Ferro on each of the three mid-May passages I made through there. I have also encountered a whiteout arriving at O'Cebreiro in early May. It was only 5 -10 cm deep, and very wet snow that melted FAST, but it did make footing difficult for a while. The whiteout only lasted about 30 minutes. These instances of snow are sporadic and widely dispersed. Just be aware... layered clothing is the best way to go.
Other than this, it is a beautiful time to walk. The flowers are plentiful, new baby animals many, and the springtime is one of the best times to walk this Camino. You will love it.
Hope this helps.