This Letter examines the electron-hosing instability in relation to the drivers of current and future plasma-wakefield experiments using fully three-dimensional particle-in-cell simulation models. The simulation results are compared to numerical solutions and to asymptotic solutions of the idealized analytic equations. The measured growth rates do not agree with the existing theory and the behavior is shown to depend sensitively on beam length, shape, and charge. We find that even when severe hosing occurs the wake can remain relatively stable.