Maybe because it shoud be "vostri cuori?" Your hearts, since you (aprite) is plural?
I think Giulio2009 is right. I mean he might be right, but it depends on the way the sentence "Open your heart!" is used in English. May the sentence "Open your heart!" be used to address a single person only or it may be also used towards a group of people? In Italian we may say both "Aprite il vostro cuore!" and "Aprite i vostri cuori!" to address a group of people, but how does it work in English?
It is the same in English, really. Heart or Hearts, when speaking to a group.
Not really. It would bug me if someone told a group to open their heart (singular). Open your hearts, group!