Hi Suz - I walked over the middle of March, started from Moissac, and it had only just been opened. Remains of some deep snow up there and some poles hidden, went from warm sunshine to seriously cold strong winds and then it stormed and snowed for an hour or so - bit worrying really, for a while.
But that was back in the year 5 and they are much more controlling of the pass now. If it is going to be rough up there it will be closed. They really do keep an eye on conditions now.
The thing is, Spring weather cannot be predicted until you get there. I have seen March like balmy spring, and have also seen it on one bad year with snow from the Pyrenees to as far as Burgos!!
Suz, you cannot pre-plan this one, keep an eye on the forecasts before you leave and then you just have to deal with the situation when you arrive and 'normally' it is lovely at that time of the year. The Valcarlos route will be open whatever as it is a highway and they plough and salt it. Of which, the pilgrim route drops off that road and back onto it many times. If weather is snow up there stay on the cleared road.
By the way, you may be arriving alone but you won't be walking alone! When you step out you will find yourself with other pilgrims, most of them first-timers and as nervous as you, is ok - all will be well.
Buen Camino!