The yahrtzeit is a day of reflection, but it is not a time of mourning per se.
The one exception is that some have the custom not to participate in a wedding (unless it's that of a very close relative) on the eve of a parent’s yahrtzeit. They would, however, participate in a wedding the night after the yahrtzeit, as well as other celebrations on the day of the yahrtzeit such as a brit milah and pidyon haben.
It is interesting to note that, the first yahrtzeit is typically the final day of the 12 months of mourning that follow a parent’s passing, and the mourning restrictions are in effect. This would not apply in a Jewish leap year, when the 12 months of mourning end a month before the first yahrtzeit.