There are many skiing areas in Julian Alps around Tarvisio - in Italy and in Slovenia.
The most known is Valbruna summit (1766m = 5794 ft) located about 10 km (6 miles) west of Tarvisio (direction Venice) - acces by ski buses or a car.
I have never been there (and to be honest I have never skiied abroad hehe) but I was talking with skiers who said that it's cheap and good place for beginners and moderate skiers.
Equipment: There are rentals of skiing and snowboard equipment in Tarvisio.
Tarvisio 2003 - the winter Universiade
XXIst Winter Universiade "Tarvisio 2003" will take place in Tarvisio and the area 14-26 January 2003.
The Universiade is an international sporting and cultural festival which is staged every two years in a different city and which is second in importance only to the Olympic Games.
The Winter Universiade consists of 6 compulsory sports and one or two optional sports also chosen by the host country, and gathered at its last edition of January in the Poprad-Tatry region, in Slovakia, a record 1.412 participants (929 athletes and 483 officials). 40 countries took part to the Slovak competitions compared to the record 48 countries of the '97 Muju-Chonju edition in Korea; where they were " only " 1.406 participants (877 athletes and 529 officials).