The Christmas season actually lasts 40 days, from Christmas Day until Candlemas, the Feast of the Presentation, on February 2. The 12 days of Christmas refer to the most festive part of the season, from Christmas Day until Epiphany.
Similarly, the period from Easter Sunday through Divine Mercy Sunday (the Sunday after Easter Sunday), also known as the Octave (or eighth day) of Easter, is an especially joyful time. But the Easter season doesn't end there: Because Easter is the most important feast in the Christian calendar—even more important than Christmas—the Easter season continues on for 50 days, through the Ascension of Our Lord to Pentecost Sunday. (Indeed, for the purpose of fulfilling our Easter Duty, the Easter season extends until Trinity Sunday, the first Sunday after Pentecost!)
So keep on celebrating and wishing your friends a happy Easter! As St. John Chrysostom reminds us in his famous Easter homily, read in Eastern Catholic and Eastern Orthodox churches on Easter, Christ has destroyed death, and now is the "feast of faith."
You can read all about Easter, including its history, practice, how the date of Easter is calculated, what holidays fall during the Easter season, and much more in Easter 101: Everything You Need to Know About Easter in the Catholic Church.