Base station (BS) sleeping has emerged as a viable solution to enhance the overall network energy efficiency by inactivating the underutilized BSs. However, it affects the performance of users in sleeping cells depending on their BS association criteria, their channel conditions towards the active BSs, and scheduling criteria and traffic loads at the active BSs. This paper characterizes the performance of cellular systems with BS sleeping by developing a systematic framework to derive the spectral efficiency and outage probability of downlink transmission to the sleeping cell users taking into account the aforementioned factors. In this context, we develop a user association scheme in which a typical user in a sleeping cell selects a BS with \textbf{M}aximum best-case \textbf{M}ean channel \textbf{A}ccess \textbf{P}robability (MMAP) which is calculated by all active BSs based on their existing traffic loads. We consider both greedy and round-robin schemes at active BSs for scheduling users in a channel. Once the association is performed, the exact access probability for a typical sleeping cell user and the statistics of its received signal and interference powers are derived to evaluate the spectral and energy efficiencies of transmission. For the sleeping cell users, we also consider the conventional \textbf{M}aximum \textbf{R}eceived \textbf{S}ignal \textbf{P}ower (MRSP)-based user association scheme along with greedy and round-robin schemes at the BSs. The impact of cell-zooming is incorporated in the derivations to analyze its feasibility in reducing the coverage holes created by BS sleeping. Numerical results show the trade-offs between spectral efficiency and energy efficiency in various network scenarios. The accuracy of the analysis is verified through Monte-Carlo simulations.