I'm using Windows 7
set time_zone = "Europe/Moscow";
Error Number: 1298
Unknown or incorrect time zone: 'Europe/Moscow'
For those who faced the same problem - here is what I found.
show variables like 'datadir'
and found out that my data files are stored in a different folder:C:\ProgramData\MySQL\MySQL Server 5.5\data\
and I was replacing files in C:\Program Files... folder initially. There was also the needed files present.
So finally everything went fine.