We examine a scenario in which the reheating temperature $T_R$ after inflation is so low that it is comparable to, or lower than, the freeze out temperature of ordinary WIMPs. In this case the dark matter relic abundance is reduced, thus relaxing the impact of the usually strong constraint coming from the requirement that the universe does not overclose. We first re-examine the dynamics of freezeout during reheating. Next we apply a Bayesian approach to study the parameter space of the MSSM with ten free parameters, the CMSSM and the singlino-dominated regions of the NMSSM. In each case we find dramatic departures from the usually considered regime of high $T_R$, with important implications for direct detection dark matter searches. In the MSSM we examine WIMP mass range up to ~5 TeV, and find regions of bino dark matter over the whole mass range, and of higgsino dark matter with mass over a similar range but starting from the ~1 TeV value of the standard high $T_R$ scenario. We show that the prospects for bino detection strongly depend on $T_R$, while the higgsino is for the most part detectable by future one-tonne detectors. The wino, which is excluded in the standard scenario, becomes allowed again if its mass is roughly above 3.5 TeV, and can be detectable. In the CMSSM, the bino and higgsino mass ranges become more constrained although detection prospects remain similar. In the Next-to-MSSM at low enough $T_R$ wide ranges of singlino-dominated parameter space of the model become cosmologically allowed. We also study the contribution to the DM relic density from direct and cascade decays of the inflaton. Finally, we consider the case of a gravitino as dark matter. We find strong bounds from overclosure and Big Bang Nucleosynthesis, and derive lower limits on $T_R$ which depend on the gravitino mass and on the nature of the lightest ordinary superpartner.