In one aspect, a system for controlling the operation of a seed-planting implement may include a ground-engaging tool and an actuator configured to adjust an operating parameter of the ground-engaging tool. Furthermore, the system may include a controller configured to control the operation of the seed-planting implement such that a primary crop is planted in a field as the seed-planting implement is being moved across the field. Additionally, the controller may be configured to determine a density of a cover crop present within the field. Moreover, the controller may be configured to determine an adjustment to be made to the operating parameter of the ground-engaging tool based on the determined density. In addition, the controller may be configured to control the operation of the actuator to execute the adjustment of the operating parameter.