I walked the Camino in March 2010. In terms of finding open alburgues, there were one or two that I came accross that were not yet opened for the season. Alternatives were always available so this was not an issue. It was a good time of year in that the alburgues, and for that matter the actual walk along the Camino, were both uncrowded.
As to weather, anything goes. Last March there were some areas of snow through the mountains, as well as strong gale force winds with rain in other places. However for the most part the days were pleasant - cool in the early mornings, turning comfortably warm and sunny by afternoon. Take a sturdy poncho along with you, and a warm pair of gloves. The cheaper ponchos can get shredded and fall apart in high wind. Obviously weather conditions vary from year to year, particulary given that March tends to be somewhat of a transitionaI period.
One of the best pieces of advice - before setting out from St. Jean Pied de Port ensure that you have checked the weather conditions for that day and that conditions are satisfactory for traveling the route that you choose to get to Roncensvalles. In bad weather this is potentially the most difficult and hazardous stage of the Camino. In good weather it is arguably the most beautiful stage and a great way to get started!
Without doubt the largest obstacle last year was mud. By March mountain snowmelt flowing along the Camino, coupled with rain made it difficult trekking in some areas. As it seems that far less snow has fallen in the mountains this year, perhaps it may be less of a hinderance for you.
In any event, you have selected a great time to walk the Camino.
Buen Camino!