Leave the car at home and use the wonderful Planai hiking buses around Schladming and Ramsau.
Buses leave from Schladming centre to Obertal and Unteral Valleys - the starts of many varied hikes. A local bus goes to Ramsau, right up the toll road to the base gondola station for the Dachstein Glacier, plus an express bus leaves from Planai cable-car station in Schladming several times per day. The buses and gondolas can be used free of charge to guests with the sumer card (Dachstein gondola once per week) The card is credit card sized, pre-printed with your details by your hotel.
Please note this summer card is free with participating hotels of the scheme. I believe it can also be obtained from the tourist board but you then have to pay. I guess hotels use it as an incentive to be booked and they probably build it into their price structure.
If you fancy a change from all the sport activities on offer in Schladming then try a trip with Taxi Maxi. I say trip but they don't do guided tours as such, more of a shared mini-bus taxi service - very friendly and helpful too. We took the round Dachstein tour. There were 6 of us in the mini-bus going to Hallstatt. We were dropped off at the ice-caves in nearby Obertraun, giving us enough time to take a guided tour and then pickerd up afterwards to spend a couple of hours in Hallstatt itself. Others went walking in Hallstatt and yet another couple opted for the salt mines ...so flexible arrangements can be made. On the way back it was a scenic tour around the area - normally a stop at Gossausee is made ...but it was the only really rainy day of our stay.
Other trips went to beautiful Salzburg (cheaper and quicker than the train., Filzmoos and Bodensee to name a few plus airport transfers. They have quite an extensive varied schedule all days of the week. No other tour operators seemed to be available in Schladming so if you don't have a car with you this is a good option.
Taxi- Maxi also own holiday apartments for rent above their offces. These looked a goog central inexpensive location to stay. Have added the weblink below for details.