Each of the horticulturalists individually decides what fertilization, if any, is necessary for their respective gardens, so I can't speak to a specific fertilization program for the Gardens as a whole. A lot of it has to do with the microclimates the Gardens provide - some areas are slightly better suited to a specific plant. The horticulturalists do water quite frequently to maintain the lush growth and diverse plant communities, but watering is also done on a garden-by-garden basis.

Unless your plants are showing signs of nutrient deficiencies, there really is no need to fertilize above and beyond what is already in the soil. The addition of extra nutrients the plants cannot take up can result in a negative effect in high enough concentrations, depending on the soil and nutrient concentrations. If you're concerned about your nutrient levels, Colorado State University does have a soil test lab where you can send samples and get recommendations based on your specific soils. Otherwise, unless the plants indicate they are missing something (stunted growth, discoloration, etc.), there is no need for excess fertilizer.