Uncovery has said it already very well.
Put winter tyres on your car. Because we had already quite some snowfall recently in Switzerland (snow has melted now), it is highly recommended that you put winter tyres on your car - as it is forbidden to drive without winter tyres in Switzerland when there is snowfall or ice on the street.
Then hit the 4 lane highway in Milano in direction to Lugano.
At entering into Switzerland, buy a highway vignette (CHF 40.-) at the border control station (Stazione doganale) which allows you to drive until the end of the year (actually until end of January of the next year) on all Switzerland's highways. If they give you already a 2024 vignette, you can drive on Switzerland's highways until end of January 2025.
Then stay on the Swiss highway in Direction Bellinzona, Zürich/Zurigo.
This will lead you finally through the Gotthard tunnel (17 km tunnel - the alternative route OVER the Gotthard is closed since mid of November 2023 because of the annual Wintersperre) and via the Axenstrasse (a short few kilometer-long non-highway passage with spectacular view to the Lake of Luzern and its surrounding mountains) to Zurich.
So the moment you pass Bellinzona, you can follow the signs on the highway which show "Zürich". You can't miss it.
If you do the driving during daylight (highly recommended) it is a very pleasant sightseeing from the moment you start approaching Switzerland until you are in Zurich.
(I did this route many times when working in Zurich and visiting my family in south France near Cannes over the weekend, driving via Genoa and Menton)
Edit: And yes, the route is always open because the problematic part (over the Gotthard) is skipped by driving through the Gotthard via the Gotthard tunnel).