The deuteron yield in Pb+Pb collisions at 2.76 TeV is consistent with thermal production at a freeze-out temperature of T = 155 MeV. The existence of deuterons with binding energy of 2.2 MeV at this temperature was described as ``snowballs in hell''. We provide a microscopic explanation of this phenomenon, utilizing relativistic hydrodynamics and switching to a hadronic afterburner at the above mentioned temperature of T = 155 MeV. The measured deuteron pT-spectra and coalescence parameter B2(pT) are reproduced without free parameters, only by implementing experimentally known cross-sections of deuteron reactions with hadrons, most importantly pi + d <-> pi + n + p.