If you fly to Krakow nearest skiing resorts on Slovakian side(2 hours) is ZUBEREC(West Tatras) or ZDIAR(east or Belianske Tatras) area.
If you look for big Slovakian skiing resorts you need to drive another hour or two to JASNA, STRBSKE PLESO, STARY SMOKOVEC or TATRANSKA LOMNICA.
Big hotels, nightlife, higher prices but it might be your cup of tea etc.
If you look for calmer experience try Zuberec. There is very good skiing in Zverovka-Spalena and another 5 smaller skiing slopes within 5-15 min drive. And you can always drive 1 hour to Jasna that have about 40 kilometers of slopes(not Alps but the best that Slovakia can offer).
Zdiar is also beautiful but I do now it well enough to offer opinion.
If you'll need advice on accomodation in Zuberec just ask.