The viral and dense deployment of small cell base stations (SBSs) will lie at the heart of 5G cellular networks. However, such dense networks can consume a significant amount of energy. In order to reduce the network's reliance on unsustainable energy sources, one can deploy self-powered SBSs that rely solely on energy harvesting. Due to the uncertainty of energy arrival and the finite capacity of energy storage systems, self-powered SBSs must smartly schedule their ON and OFF operation. In this paper, the problem of ON/OFF scheduling of self-powered SBSs is studied in the presence of energy harvesting uncertainty with the goal of minimizing the tradeoff between power consumption and flow-level delay. To solve this problem, a novel approach based on the ski rental framework, a powerful online optimization tool, is proposed. To find the desired solution of the ski rental problem, a randomized online algorithm is developed to enable each SBS to autonomously decide on its ON/OFF schedule, without knowing any prior information on future energy arrivals. Simulation results show that the proposed algorithm can reduce power consumption and delay over a given time period compared to a baseline that turns SBSs ON by using an energy threshold. The results show that this performance gain can reach up to 12.7% reduction of the total cost. The results also show that the proposed algorithm can eliminate up to 72.5% of the ON/OFF switching overhead compared to the baseline approach.