As an aveil, I was told that I could not take part in the hoshana circuits, nor dance with the sifrei Torah on Simchas Torah. Why is this not counted as public mourning which is forbidden on Shabbos and Tom Tov?
There are many poskim who say that things that an aveil doesn’t do during shloshim and he mourning year are not subject to the restriction of not mourning in public, and are still observed. The reason for this is that the aveilus of seven days are real acts of mourning, such as sitting on the floor, however what an aveil abstains from during shloshim and 12 months are only acts of honor for the deceased, and not acts of real active mourning. Therefore there is no prohibition with doing them during the shloshim and 12 months.
Shach Y:D 393-7, 400-2, Gra Y:D 393-10, 399-4, Mahari Veil -5, Divrei Sofrim- Avelius 393 Birur Halacha, D:H Vyesh Omrim, paragraph V’ hata’am