Hello Fodorites, I need your help again please!
We will be in Italy in August, and plan on taking the earliest train from Varenna to Tirano (then catch a train to Chur) on Aug. 15, a public holiday in Italy. Does anyone know if the regional trains run full schedule on public holidays? Thanks!

Sometimes in August they add some extra runs. Trenord doesn't seem to have summer schedules loaded yet, but since the changeover is 6/15, I would wait until then and try your dates. There are trains that require changes and trains that don't and typically schedules don't change much.

http://www.trenord.it/EN/

On the 15th, Ferragosto, they run a holiday schedule. It would be similar to the Sunday schedule, or to the May 1st schedule. You could have a look at those to get an idea, but then check again after the schedule change.

Varenna dp 7.24 - Tirano 8.50/9.40 - Pontresina 11.50/12.02 - Samedan 12.08/12.17 - Chur ar 14.03
or
Varenna dp 7.24 - Colico 7.47 - Chiavenna 8.34/9.08 - St. Moritz 10.51/11.02 - Chur ar 13.03

The early morning connection Varenna dp 6.38 - Chiavenna 7.37/7.50 - Splugen 9.40/9.53 - Chur ar 10.45 is NOT possible on August 15th because the train Varenna dp 6.38 will not run.
The train Varenna dp 7.53 - Tirano ar 9.56 will fall out too.