Nauders in Jan

Hi!
Welcome to the forum!
Your question is very specific, not the typical type of question we see on this forum, which tends to be aimed at American travellers (not exclusively, but mainly) planning sightseeing trips to Europe.

What I do know, is that winter tyres are mandatory in Austria in winter - but isn't it the case in Germany as well? In my admittedly limited experience, whether they are sufficient in heavy snow entirely depends on your type of car... But the road to Nauders is a fairly important route to Italy so I wouldn't worry too much.
As for traffic, the Füssen route is prone to traffic jams - the road through Imst can be a crawl! The Arlberg tunnel approach can be slow too, but not as bad as far as I know.

Hi,

Thank you. Winter tyres are required in Germany, but such heavy snowing are rare and not a common occurrence in the south, hence i do not have any snow chains with me.

I will take the Arlberg tunnel, you are right Fuessen will have a lot of traffic towards Italy. It should be safer during bad weather.

Maybe this offer is for you:
https://www.adac.de/der-adac/regionalclubs/landingpages/schneeketten/

The last section of the road, when you need to climb about 500 meters altitude from Inn valley via some steep sections and serpentines up to Nauders is the critical one.
In case of snowfall there is a realistic chance that snow chains are made compulsory by the following road sign. https://www.oeamtc.at/thema/vorschriften-strafen/schneeketten-was-ist-bei-der-verwendung-zu-beachten-16185446
In case you don’t have snow chains you would need to leave your car somewhere and take a Taxi or the public bus for the last ascent.
Maybe you talk to the landlord of your accommodation if they would pick you up in that case.

The risk-free option is the ADAC offer posted by wmt1.