The implementation of uplink HARQ in a Cloud- Radio Access Network RAN (C-RAN) architecture is constrained by the two-way latency on the fronthaul links connecting the Remote Radio Heads (RRHs) with the Baseband Units (BBUs) that perform decoding. To overcome this limitation, this work considers an architecture based on the separation of control and data planes, in which retransmission control decisions are made at the edge of the network, that is, by the RRHs or User Equipments (UEs), while data decoding is carried out remotely at the BBUs. This solution enables low-latency local retransmission decisions to be made at the RRHs or UEs, which are not subject to the fronthaul latency constraints, while at the same time leveraging the decoding capability of the BBUs. A system with BBU Hoteling system is considered first in which each RRH has a dedicated BBU in the cloud. For this system, the control-data separation leverages low-latency local feedback from an RRH to drive the HARQ process of a given UE. Throughput and probability of error of this solution are analyzed for the three standard HARQ modes of Type-I, Chase Combining and Incremental Redundancy over a general fading MIMO link. Then, novel user-centric low-latency feedback strategies are proposed and analyzed for the C-RAN architecture, with a single centralized BBU, based on limited "hard" or "soft" local feedback from the RRHs to the UE and on retransmission decisions taken at the UE. The analysis presented in this work allows the optimization of the considered schemes, as well as the investigation of the impact of system parameters such as HARQ protocol type, blocklength and number of antennas on the performance of low-latency local HARQ decisions in BBU Hoteling and C-RAN architectures.