Essentially your issue is that you have extra data specific to the term and WP doesn’t natively store such data.
On top of my head the low hanging ways to make it would be:
- Maintain the list of schools/colors and whenever school term is assigned automatically assign respective colors by code.
- Create term metadata tables (which would work via regular Metadata API, just not provided natively, there are plugins that take care of setup) and store information about colors as meta information in school terms, retrieving as necessary.
However if this is just one case of many similar requirements, you may want to implement schools as custom post types and add post relationships implementation to handle connections. Taxonomies are by nature grouping mechanism and aren’t engineered to be data–heavy.