In reply to Dan Bailey - UKHillwalking.com:
I walked Stage 2 of the HRP last July and it was only the Port du Lavedan (ice field) and the Col de Fache (slushy snow) that proved tricky; crampons were necessary for the PdL, we took the variant route. Refuge Wallon (avoid like the plague!) to Refuge Baysellance was free of snow but a week earlier apparently also required crampons and axe.
There was late snowfall last year and apparently a lot more snow hung on than normal so given the lean winter just gone, I wouldn't expect there to be much left come July.
P.S. definitely stay at Refuge d'Arremoulit, it's beautiful!