Well, I went East to West, from Perpignan to St. Sebastian and so on, staying on the French side. My recollection was three major cols and, I think one more that had too much snow even to push the bike through. It was at least as fine, in every possible way, as any bicycing I've ever had. As for the long climbs, it shouldn't be any bother at all. Have gearing low enough that you can go very slow, even very, very slow, then just take your time, enjoy the incredible scenery, and before you know it you'll pop out on top. Go for it!!!!

PS Oh yes, everyone needs to have their bikes in perfect maintenance, new tires, adjusted brakes etc. You don't want anything to go wrong on the way down. And that, btw, will be equal to any other finest experience you've ever had.