Skiing near Salzburg

Schladming is a good one, quite extensive, with a train station right at the resort and decent travel times from Salzburg (90 minutes), but there are probably some nearer options.

Do you travel by public transport or by car?
If you plan a night in Gosau you could combine a visit to Hallstatt and skiing.
https://www.skiresort.info/ski-resort/dachstein-west-gosaurussbachannaberg/

Easiest to reach by public transport:
Bad Gastein – 1:30 by train. There is a cable car directly at the train station.
https://www.skiresort.info/ski-resort/bad-gasteinbad-hofgastein-schlossalmangertalstubnerkogel/
Zell am See – 1:30 by train.
Ski area Schmittenhoehe is in walking distance from the train station. https://www.skiresort.info/ski-resort/schmittenhoehe-zell-am-see/
Or you take Buss 660 for another 30 minutes to Kaprun Kitzsteinhorn (it the highest possible resort for a daytrip from Salzburg).
https://www.skiresort.info/ski-resort/kitzsteinhornmaiskogel-kaprun/

Hochkoenig – 1:30 by combination of train (Bischofshofen) and bus 590.
https://www.skiresort.info/ski-resort/hochkoenig-maria-almdientenmuehlbach/

There are many more. Here you can find a list of ski resorts in Salzburg.
https://www.skiresort.info/ski-resorts/salzburg-salzburger-land/

I was going to recommend the ski bus service we used one year. It left from Salzburg daily, with a rotating list of what resort on what day of the week. There was an English speaking guide on the bus who gave us directions how to purchase lift ticket, rent skis, get oriented on the mountain for your skill level, etc. which is helpful for a first time Europe skier. But my internet research tells me they are out of business. But I did find this: https://www.snow-space.com/en/winter/information-ski-resort/service/skibus-skidepots where it appears you can get free public transport if you purchase lift tickets on line in advance.

I am not a skier, but this summer we stayed at Oberauer Wagrain - Die Hotelpension (B&B), in Wagrain, which is a ski resort in winter, and we loved it. It’s close to both Salzburg and Hallstatt.

You plan to pack all your ski clothing (gloves, ski pants, ski jacket)?

Ski jacket an be used as your regular walking around jacket as well, not something extra that needs to be packed.

Sam, of course it can but I wouldn’t.

But that is because you live in Austria. I have done it every time I've gone to Europe for skiing and then additional touring afterward. And that is about 2 dozen times.

Yes, if you are coming to Austria to ski for a week, then of course you bring your ski jacket. But for an afternoon of skiing?

My point is that if you are going to northern Europe during ski season, you are going to need a warm coat, and a ski jacket works fine for that purpose.

My skiing days are over, but I would want to bring my own kit. If you are able, you could buy cloths here and send back and rent skis and boots. Yes, you will pay top dollar, but you will have it home. Make the best of it. You could even do ebay.de/at and maybe send to your hotel?
https://www.skiamade.com/en