We walked up to the col from bourg st pierre on 18th june last year. There were still patches of snow across parts of the path, we crossed some but the last bit was such that we had to walk the final bit on the road with traffic coming by - not ideal but it was ok and we had nice chats with motorcyclists and cyclists who had stopped for the spectacular views. I was nervous crossing some stretches of snow, thinking they might give way under my feet but using poles gave me confidence. The worst patch was descending the following day but we could have retraced our steps and gone down the road if i really decided i wasnt going to risk it - there were people skiing down some of the gullies. I am not a brave soul but felt quite proud of myself doing that, though my walkng partner wasnt the least bit concerned so it depends on your view.
We stayed overnight but there is very little at the pass, it was the walk up and the descent which was the best bit. We stayed then at etroubles before moving on to aosta, in fact stayed just beyond there at chatillon. The walk to aosta was great too, walking alongside the ru’s, the old irrigation channels. For me being in the mountains was wonderful, especially as you then enter the po valley and flat landscape for some days.
If you can walk from lausanne then do, the swiss bit of the vf was lovely, walking along the lake then through wildflower meadows.
Have a wonderful time.