It shall be unlawful to drive any vehicle or animal or to allow any vehicle or animal to proceed on or over any garden, lawn, sidewalk, beach, wall, or any other portion of such public place as described in Section 9.19.040, Provo City Code unless the same are designated for vehicular or animal traffic. It shall be presumed for the purposes of this Chapter that in any area in use at the time as a picnic or recreational area or otherwise in use by pedestrian traffic that the same is prohibited for use by vehicular or animal traffic. This paragraph shall not be construed to prohibit the presence of dogs and cats and similar other small animals while under the control of their owners from being allowed upon such public property unless such are vicious and are shown such either by their general nature or by the facts of the case.