In the face of heightened societal interest in decarbonization, wind energy is emerging more and more as a viable, low-emission source of clean power. Unlike stationary wind turbines, mobile wind turbines (MWTs) possess the ability to be transported by truck, supplying electricity to power distribution systems (DSs). This spatiotemporal flexibility offers notable advantages, especially in enhancing system resilience following extreme natural disasters. However, the full potential of these resources remains untapped, underscoring the need for enhanced utilization strategies. In this paper, we develop an optimal scheme for strategically dispatching MWTs to enhance the resilience of the DS accounting for the uncertain predictions of wind energy. A joint chance-constrained programming (JCCP) model formulated as a mixed-integer nonlinear programming (MINLP) problem is introduced to capture the uncertainty in wind energy forecasts. We develop a linearization method that are computationally feasible, allowing us to transform the MINLP model into an equivalent mixed-integer linear programming (MILP) formulation. Case studies conducted on the IEEE 123-node test system illustrate the efficiency of the suggested service restoration strategy in enhancing the resilience of the DS during extreme events.