Magnetic topological insulators combine nontrivial band topology with magnetic order, enabling exotic phenomena such as the quantum anomalous Hall effect (QAHE), axion insulator, and Majorana states. EuSn2As2 is proposed as a candidate for an intrinsic magnetic topological insulator, based on first-principles calculations and angle-resolved photoemission spectroscopy (ARPES) experiments. Recent theoretical studies reported pronounced dimensionality-dependent magnetism and electronic structure in EuSn2As2. However, owing to its relatively strong interlayer coupling, experimental investigations of few-layer EuSn2As2 remain absent to date. Here, we report a systematic investigation of the thickness-dependent magnetic and transport properties of EuSn2As2 flakes approaching the two-dimensional limit. Thick samples exhibit bulk-like behavior, including classical metallic transport and exponential negative magnetoresistance (MR). In contrast, ultrathin samples display insulating behavior with linear negative MR. Measurements of MR and the anomalous Hall effect confirm the preservation of long-range magnetic order down to an atomically thin insulating regime. Phase diagrams mapped from the experimental data illustrate a monotonic suppression of both Néel temperature and the saturation field with decreasing thickness. Our results demonstrate that EuSn2As2 retains robust magnetism and undergoes a metal-insulator transition in atomically thin samples, providing a platform for realizing exotic quantum states, such as QAHE, and for exploring device functionalities in quantum information technology.