Faistenau is a small town just 15 km away from Salzburg and usually offers from December to March several cross county skiing trails. Thanks to good public connection, buses from Salzburg take around 40 min and leave every 30 min, it's a very reasonable trip with public transports. Especially from central and eastern Austria in connection with a half day stay (or longer) in Salzburg. Faistenau is the highest elevated town of the Flachgau region, located on 800 m and therefore quite a snow-sure area (till earth temperature rises even more).
I started from Linz in the morning. Theoretically, there are closer cross-country areas, but either they don't have public connection (Böhmerwald) or are rather low in the alpine valleys. Therefore, Faistenau in combination with a Salzburg day trip is not that unreasonable, even from Vienna.
Changing in Salzburg and bus takes 42 min. Thanks to a recent push to promote publics, bus leaves every 30 min. After 2-4 h of sports, just take a bus back to Salzburg, spend the afternoon there and then take a train back home. The bus from Salzburg to Faistenau is for winter sports even for free, bringing equipment shows is, I suppose if you tell them, that you are going to borrow the equipment it works as well.
From the bus station Faistenau Mechaniker Wörndl it is a 1 min walk to the ski rental Schuh Sport Auer (entrance bit down the road the to right of the front of the building). The price for the cross-country slope you can pay right at the entrance with card at a machine (in 2022 it was 9€), a map is available online or just at the rental store. On their homepage they publish every day in the morning the recent conditions, for trying it is enough if some parts are marked with orange. Means not ideal conditions, but it works. A lot of green parts are obviously nicer, as this guarantees a proper winter landscape. At the Volksschule Faistenau you can change, have lockers and shower as well, 10 min walking from the rental shop.