almost all trains run all the year :) There are just few seasonal trains to touristic spots as direct trains (The Cities are still reachable in off season but with more changes ) :)
For example in summer a Nighttrain from Vienna to Split or Budapest to Rijeka/Koper :)
Only excpetion in my experience is the Train Belgrade - Skopje - Thessaloniki that operated since years just in summer :/ (Actual still not back in service due the pandemic :/ )