Never thought I'll personally say something like this, but capitalism and west completely changed (screw, if you ask religious people) the view on Christmas and Easter. Bunny/rabbit was never connected to Easter here on Balkan. Santa got here because of Coca-Cola. We (Christians around here, count me out) celebrate Christmas as a Jesus Christ's birthday even though we do not think he was born on that day. Easter is about Christ's resurrection and while rabbits weren't tied to the celebration, eggs were. Beats me why, when I cared I didn't have internet and those that I asked said something along the "eggs == new life". EDIT: Quick search tells that eggs, as well as fertility and rebirth in general, simbolise Christ's empty tomb for Christians.
Sanguinala Saturnalia was being held from 17th to 23rd December and some Pope decided "lets celebrate Christ's birth on 25th" since it's close to a major celebration and it'd be easier to make others "switch" religion aka sound business decision.