Right now promotions are not fieldable entities, and are not easily altered to store additional data in them.
This would not be a huge problem, but the promotion offers are not entities at all, and the data about which conditions the promotions applies to are thrown into serialized blobs, so it is impossible to query offers and promotions that match particular conditions.
Ideally, offers would be made into their own entities, with relations to things like product variations stored in actual data relationships so they can be queried. However, in the meantime making promotions into fieldable entities would allow them to have additional data added to them so they could be queried in cases like views filters.
Active
2.0
Contributed modules
Here is a patch that adds a simple stub config page for promotions, so that the field api can add tabs to manage fields and the form/display settings.
This started by a request to make promotion offer entities... But in the end you're patching Commerce to expose the field UI for the Promotion entity type...Should we repurpose this issue?