In recent years, the urban heat island (UHI) effect and frequent heatwaves have become escalating threats to metropolises. Vegetation's cooling services and their equitable access have gained attention for mitigating extreme heat and promoting environmental justice. However, the characteristics of vegetation cooling services along the urban-rural gradient and among different population groups require further investigation. This study focuses on Shanghai to investigate cooling service exposure and equity patterns. Using the Heat Mitigation Index (HMI) from the newly LAI-integrated InVEST urban cooling model as a proxy for vegetation cooling services, as well as the Gini index as the indicator of equity, we analyzed cooling exposure and equity across the urban-rural gradient and among different population groups at multiple levels. The results indicate that: 1) Integrating Leaf Area Index (LAI) improves HMI simulation accuracy by enhancing heterogeneity within green areas and strengthening the correlation with land surface temperature (LST) by up to 67.5 %. 2) Cooling service exposure and inequity display a clear urban-rural gradient, with residents in central areas enjoying lower but more equitable cooling services, while those in peripheral areas experiencing higher but less equitable services. Specifically, the average cooling exposure, measured on a normalized range from 0 to 1, increases from 0.130 in the Inner Urban Area (IUA) to 0.211 in the Outer Suburban Area (OSA), and the Gini index rises from 0.298 to 0.486 from the inner to the outer ring, indicating greater inequality in peripheral. 3) Gaps in cooling service exposure and equity among population groups, based on age and local status, are widening along the urban-rural gradient. These findings enhance our understanding of vegetation cooling service distribution in large cities and underscore the need for targeted planning and support for vulnerable groups to promote environmental justice.