Styrian police said the refugees were supplied with woollen and thermal blankets and warm drinks.
More than 6,000 refugees arrived in Styria on Wednesday and in the evening around 2,000 people were taken to emergency shelters in Graz and other Austrian states by bus.
Police said that the situation on the border was “under control” and that barriers had been opened to let large groups of people through and avoid injuries.
Some 900 refugees arrived in Bad Radkersburg on Wednesday evening and were taken to emergency accommodation.
Several thousand more refugees and migrants are expected to cross the border into Austria on Thursday.
The Red Cross has asked people not to bring donations to the border crossing at Spielfeld. Donations of food - such as bread, bananas and still mineral water - should be taken to the former Euroshopping centre in Graz-Webling. Donations of clothes should be taken to Caritas centres.
The Red Cross has warned that with temperatures dropping the situation is becoming "critical". "We are doing everything humanly possible to make sure that people receive help at the border, and of course we are especially concerned for the children," spokesman Christopf Patzalt said.
Police in Germany have complained that Austrian authorities often bring large groups to the border in the late afternoon or evening.
"It's no problem up until midday. But in the late afternoon, it's blow after blow. Our Austrian colleagues are just as overloaded as we are," Freyung district police spokesman Thomas Schweikl said.
On Wednesday, Austria’s interior minister announced plans to build a fence at the border crossing with Slovenia to "control" the refugee influx, but this prompted sharp criticism from Berlin, underlining how the crisis is straining relations within the EU.
EU officials said they were not told in advance of Austria's plan and in a sign of the sensitivity of the development, European Commission President Jean-Claude Juncker held hastily arranged talks with Austrian Chancellor Werner Faymann.
Afterwards the two men issued a statement apparently seeking to stress common ground. "The president and the chancellor repeated their common position that fences have no place in Europe," the statement said.