Very glad you asked this question. It's difficult to know just how dangerous or extreme the pass will be...for oneself. What's not do-able for one person might be very do-able for the next. We are winter hikers who are used to subzero temperatures and deep snow; we routinely hike 4000+ ft elevation gain and 10-15 miles in the mountains during the winter in our home state of New Hampshire. We are starting in March 2013 from SJPP and would like to cross the Pyrenees. I worry a bit that the officials will advise against it when the conditions would be well what we are used to. In addition, they may be conservative in their advice when they look at my two daughters...but my two kids are experienced winter hikers with well over 100 mountains each under their belts. Also, I have a feeling "cold" for northern Spain feels like business-as-usual to us. We'd like to cross as long as visibility is reasonable and route-finding isn't a challenge.
All that being said, I don't want to underestimate the region since I have zero experience hiking this particular pass. I guess that once we're there, we'll check the forecast, ask around, and make the decision.
A thought -- One could always turn around and come back down to SJPP if the conditions start to feel treacherous (bring a compass), then do the Valcarlos route instead. Would lose a day, but that might not be too big a deal in the grand scheme of things.