You are correct about Christmas, but incorrect about Easter.
The celebration of the birth of Christ was randomly selected because his actual birthdate was unknown. Indeed, many Christian sects give only a secular nod towards Christmas.
However, there is no randomness in the date Easter is celebrated. Christians have convened hundreds (thousands) of times to pour over the records and scriptures to determine the historical accuracy and timing of the events leading up to the Resurrection of Christ. Easter is tied intimately to coincide with Passover and attempts to stay as closely timed with luna events as possible.
The ecclesiastical rules are: Easter falls on the first Sunday following the first ecclesiastical full moon that occurs on or after March 21 (the day of the ecclesiastical vernal equinox). This particular ecclesiastical full moon is the 14th day of a tabular lunation (new moon).
That's a very pagan way of setting a celebration date -- which can be any Sunday from March 22 to April 25 inclusive. And the ecclesiastical full moon is not the same as the real full moon. It might not be random but it sure seems that way: plus or minus two and a half weeks.
Why not just celebrate it on the real Vernal Equinox?
Why does Eastern Christianity's dates for Easter not agree with Western Christianity's dates. They may be the same or over a month different! In Eastern Christianity, Easter falls between April 4 and May 8 between 1900 and 2100 based on the Gregorian date.
At least Kwanzaa has a set date.