The reception was designed to congratulate their contribution to Irish arts and culture.
Other artists in attendance were Neil Hannon, Mundy, Emmett Tinley and members of The Frames.
BellX1, currently on the very top of the Irish chart album with Flock, were invited but unable to make the gathering due to tour commitments.
Gary Lightbody, frontman of Snow Patrol, told hotpress.com: "We got this letter telling us we were invited to meet the President. We're actually in the studio in England [recording the follow up to the hugely successful Final Straw] but we said yes."
"When we went to shake her hand, and she said that our album gets played in their house loads. I'm assuming it's by their kids, I can't imagine that they'd listen to it!
"She then made a speech thanking us for making our music, poetry and books."
Asked whether he expected the invite, Gary, who spent four years in Snow Patrol before their two-million selling album, said: "I doesn't surprise me, but nothing surprises me anymore."