I was there early May, and there still was snow in the mountains ! The Ski season is from December to April or May, depending on the winter. It'll still be rather cold when you go, make sure to bring warm clothes for the mountains.
I only spent one evening to the next morning there, in Tatranska Lomnica, so I can't help you much. I've found this link to give you more infos : High Tatras - Slovakia
. I can tell you it was gorgeous, and yes, it is worth staying a few days !