Here's a link to a map clearly showing the main acces roads (e.g. motorways) likely to stay open all year round despite adverse weather.
From West to East, clockwise :
Nice, Frejus, Mont Blanc (tunnel has toll) , Simplon/Sempione, St. Gothard and St. Bernardin (both converging at Bellinzona level in the Italian speaking Swiss Canton of Tessin/Ticino), Brenner ("Europa" bridge subject to toll as well), Tarvisio and Trieste.
Main roads throught Alps to/from Italy
A word of warning, all are subjected to tolls of some sorts. The swiss motorways have a "vignette" system (valid for 14 months, from beginning of December of the year N-1 to end of January of year N+1), it can be, from this August, purchased also via a website. The cost is about 40 CHF.
The Austrian ones as well, but give the option of 10 days (9,90 €) , two months (29,00 €) and one year (96,40 €). The Slovenian one 117,50€ for the whole year, 32€ for one month and 16€ for a week...
Italy and France are "pay-per-drive"...paying when exiting at the toll station, the more km one drives through a motorway the higher the toll...