I think you might be lucky to get over it. On tuesday I did the Klausen, St Gottardo, Grimsel, Furka, Susten and Oberalp passes.
It was 26° in the valley, but cold up at the top. The Grimsel has had snow already but most is melted. Officially i don't know how long they keep the passes open for ... but one big dump and it might be next June before you get over them !! ( well, it was this year)
Why do you think I was asking about heated waistcoats elsewhere.......................?
I'm in that part of the world anyway, so if it's open I'll ascend, if not, I'll move on......the last time I was there was on an RT, two up with as much luggage as it would carry.......and it was hot & crowded!!
I was thinking solo on a GS might be fun........even if it's a bit chilly..............