Euro routes. E2/GR5 is reasonably high, but no transalp routes (they cross)
Altitudes via Color coded map
Aim for skiable conditions: March, April to early May in places.
Some guy: " With this in mind you will want to go when the huts are open and staffed, roughly from the 3rd week of March through mid-May. "
Me: May/June had snow about 2500m
Need snow to 2000m for skiing, to avoid hgiher areas with glaciers. At elevations above 1,500 m almost all precipitation in winter falls as snow. Snow usually lasts from November until May at the (2,000-m) level,
Conclusion: April to mid May ; except snow line at 1500m to 2000m
RED Via Alpina
Start at Mont Bego ... travel to Risoul / Mont Viso. 8 days travel ... say 2 weeks including getting there.
Then bus/hitch to vanoise
Modane to Aostra -> make our way through vanoise and paradiso. exit at aosta.
note: red route from valoise to chamoix is pretty low:
HAUTE ROUTE : chamois to zermat
We like to leave Chamonix on a Sunday and arrive in Zermatt on a Friday as it gives us the best chance of having quiet huts along the way. If you want solitude and a higher possibility of good snow then look at late March or early April and ski mid-week to avoid the crowds during the trip.
"Classic": more mountaineering, less traffic. 1 week.
Both of the above have a break on day 2 (taxi)
Grand Lui is longer and no break
"There is no glacier walking except for one narrow glacier that in normal circumstances can be treated merely as a snow patch, and there is no rock climbing. "
From Bageres /Mont Fort to entry to Zurmatt Valley it's high. Looking here http://www.gpsvisualizer.com/display/20180219203812-43252-map.html it looks feasible to ski cabane to cabane on and of the route, below the glaciers.
From Zurmatt Valley it's mixed to Bernina. http://www.gpsvisualizer.com/display/20180219205231-43252-map.html
North of Lake Como, probably too low, head to Sondrio and continue to Bernina.
After this, red heads north and low - continue east to bolzano
Chamoix asoc of guides: