Fuh, nothing nation-wide like that for Slovakia comes to my mind.

The closest are probably multiple jarmok-s (fairs) that happen in towns at the end of the summer/beginning of fall. In my hometown of Bardejov the jarmok is one of the main events of the year. It’s said that if you want to meet your old pals from high school, do it during Christmas or during jarmok because for those dates everyone travels home

Edit Eh, and Pohoda Summer festival I guess. I personally don’t like it but I must admit it’s a thing and some people take it almost religiously