Ski-park Jasná, Low Tatras
The best skiing area of Slovakia is in the Low Tatras and is called Jasná. Most certainly you will find snow there from December till April. Slovakia has a continental climate, thus winters are colder than in Western Europa.
Ski-park Jasná is suitable for all kinds of winter sports, for beginners to professionals. The best time of the season is January and February. One avoids the busy season of school holidays in Slovakia that last from the end of Februari till half of March; moreover prices of accommodation are a bit lower then.
You will find hotels and pensions in all categories. In the hotels it is mostly possible to hire skiing equipment and to buy a ski-pass with discount. And if you would like to take a break from skiing, you may always relax in the thermal and aqua parks of the surroundings.
Beware that you are obliged in Slovakia to have snow tyres at snowfall. If you are arriving with public transport: there is a good train connection from Bratislava to Liptovský Mikuláš, and from there a free bus is leaving to the ski-park each half hour.