Yes, of course you can do that using the remotely sensed data (Landsat TM & ETM+, SPOT, ..). The vegetation indices such as the NDVI, SAVI, MSAVI2 and the soil/vegetation moisture indices such as the Tasseled Cap Wetness indicator (TCW) could offer very powerful tools to investigate and assess the health of rangeland. Applying the vegetation density classification and change detection techniques then will lead to knowing the impacts of the high grazing intensity in your study area. Good luck.

Yes... NDVI is perhaps better surrogate; SPOT veg at 1KM resolution and MODIS vegetation indices (1Km, 500m and 250m resolution) can be very helpful in this regard. Time series analysis can be performed on these hypertemporal data to find out trends in vegetation. may be you can find TIMESATS and interesting software for these sort of analyses

I think NDVI is better. You can use the widely-used processed NDVI datasets from AVHRR GIMMS NDVI archive datasets which spans from 1981 to 2006