Radio Slovakia International started broadcasting in 1993, the year it broke away from the Czech Republic and ended Czechoslovakia as an entity. It is leaving shortwave at the end of 2010 but retains internet and satellite broadcasts.
National radio is from Slovensky Rozhlas, part of the group who bring us Radio Slovakia on shortwave. Their QSL gallery is worth a look, covering all the cards issued by the station in their ten years of existence. The 2002 set of Czech radios is especially creative: http://www.slovakradio.sk/
The Tatra mountains in Slovakia don't make it into the Top 100 Snowboarding and Ski resorts guide, but they have long provided good skiing. Starý Smokovic is one such ski town, and from there an hour on a narrow gauge railway takes you from 1025 metres up to Strbske Pleso at 1355m, which was a top ski resort in the 1930s. The Grand Hotel there can be seen at: http://www.kempinski.com/en/hightatras/Pages/Welcome.aspx and they have a Facebook page.
There is an outlet of Lumen Radio in Strbske Pleso: http://www.lumen.sk/
Many moons ago as independence dawned on Slovakia, I bought an Olympia radio in the small Prior Department store in Strbske Pleso for 880 Slovak crowns (£19). The box said it was made in Taiwan, the radio's label stated India. Either way, this mw, sw, lw, and fm receiver served me well as a robust pocket portable for ten years, before its demise.
Local radio in the area may inform you of weather conditions on the ski slopes. Radio Expres 96.5 , Radio Zet 84.5 and Radio Frontinus 104.6 cover the region:
National station Radio Twist became Radio viva and also has outlets in the Tatra regions towns of Kosice and Zilina: http://www.radioviva.sk/ Another popular national station that has been running for nearly two decades is Fun Radio. Western European pop merges with eastern at: http://www.funradio.sk/ Both stations have live webcams so you can see what's going on in the studio.