Game of Thrones / ASOIAF Theory: Are Jon and Daenerys Twins ?

Due to popular demand and many comments and questions here I discuss if Jon Snow and Daenerys Targaryen are perhaps twins. Or even just siblings. Were they both born at the Tower of Joy by Lyanna Stark and Rhaegar Targaryen? Or perhaps they are siblings born at separate times, is this possible in the timeline? Discuss!