Low-power wide-area networks (LPWANs) have received extensive attention from both academia and industry, since they can efficiently provide massive connectivity to internet of things (IoT) devices in wide geographical areas with low cost and low power consumption. Recently, it was shown that macro-diversity among multiple gateways significantly improves the performance of uplink LPWANs by coherently combining multiple received signals at gateways. We call such networks cooperative LPWANs. In this paper, the error performance of an uplink cooperative LPWAN is mathematically analyzed in terms of outage probability, bit error rate (BER), and diversity order. It is assumed that there exist multiple (two or more) gateways that have multiple antennas and are located at arbitrary positions in the LPWAN area. Each gateway exploits the optimal maximum-ratio combining (MRC) technique to decode the received signal, and then the signals after MRC are delivered to the cloud fusion center for coherent combining in the cooperative LPWAN. The main results, the closed-form expressions of outage probability and BER, were derived by utilizing the hyper-Erlang distribution. Furthermore, the macro-diversity order was mathematically derived. The mathematical analysis was validated through extensive computer simulations. It worth noting that the mathematical analysis of the error performance of cooperative LPWANs is the first theoretical result in the literature to the best of our knowledge.