Hmm. I found this page
http://www.circumetnea.it/linee_orar...GEN%202018.pdf that has the schedule for January 2018 without much trouble. Note that the train does not run on Sunday and holidays.
So if it is running in January, it is most likely running all winter.
The main page is here
Ferrovia Circumetnea | Linee e Orari
And while the page says January 2017 the link seems to indicate 2018.