Load-altering attacks (LAAs) pose a significant threat to power systems with Internet of Things (IoT)-controllable load devices. This research examines the detrimental impact of LAAs on the voltage profile of distribution systems, taking into account the realistic load model with constant impedance Z, constant current I, and constant power P (ZIP). We derive closed-form expressions for computing the voltages of buses following LAA by making approximations to the power flow as well as the load model. We also characterize the minimum number of devices to be manipulated in order to cause voltage safety violations in the system. We conduct extensive simulations using the IEEE-33 bus system to verify the accuracy of the proposed approximations and highlight the difference between the attack impacts while considering constant power and the ZIP load model (which is more representative of real-world loads).