... it's difficult to forecast so long in advance what the weather will be. For example, today all the area in the Catalan Pyrenees and the pre-Pyrenees (the zone prior to reaching the mountain ranges themselves) is all snowed and/or wet (lots of rain yesterday and today): http://www.ccma.cat/el-temps/divendres-torna-lhivern-pluja-neu-vent-i-mala-mar/noticia/2833638/
Theoretically, by March there's still snow in the high peaks but the weather should have improved, however, I would like to point out that from time to time we have snow on the coast as well thus if you have snow by the seashore you can imagine how the small roads in the Pyrenees must be.
In 2010 Barcelona saw a heavy snow for a day or two. For those that have visited already, you might find curious to see familiar sights like the Sagrada Família, the Magic Fountain, Park Güell or Tibidabo all snowed: https://goo.gl/photos/Nj681rTb4R3CKcgM9
Then, you say you have explored the areas of the Aragonese and French Pyrenees, have you had a peek at the Catalan Pyrenees? Maybe they can catch your eye. Without demereting Jaca or Ainsa, the Catalan Pyrenees have a few advantages in your case: firstly they're closer to Barcelona, thus faster and easier reach; secondly in case of really bad weather, you can reach a main road ('main' is in interstate-like) with more ease so you wouldn't get stuck; and thirdly, there are also many nooks and crannies in this part of the Pyrenees equally worthwhile for exploring.
Just in case you'd like to consider it
And if you are fan of visiting UNESCO sites, la Vall de Boí (the Boí Valley) contains some of the Romanesque gems of Europe. For more info here.
Enjoy!