In one aspect, a system for determining soil parameters of a field across which an agricultural implement is being moved may include a sensor mounted on a ground engaging member. As such, the sensor may be configured to capture data indicative of a soil parameter of soil within the field. Furthermore, the system may include a controller configured to receive an input indicative of a selected planting depth for the field. Moreover, the controller may be configured to control an operation of an actuator in a manner that adjusts the penetration depth of the ground engaging member such that the sensor is positioned at the selected planting depth. Additionally, the controller may be configured to determine the soil parameter of the soil within the field at the selected planting depth based on the data received from the sensor.