I think you might also want a table with a record for each Track as well.
What you describe is actually a "many to many" relationship. A given horse can appear in many races and any given race lists many horses. Thus, neither an ID that uniquely identifies each race nor an ID that uniquely identifies each horse is sufficient to set up the correct relationship. You need both, plus an additional table that we call a "join" table that manages the resulting many to many relationship.
Start with these relationships:
Races::__pkRaceIDID = Race_Horse::_fkRaceIDID
Horses::__pkHorseIDID = Race_Horse::_fkHorseIDID
You can place a portal to Race_Horse on the Races layout to list and select a Horses record for each given Races record. Fields from Horses can be included in the Portal to show additional info about each selected Horses record and the _fkHorseIDID field can be set up with a value list for selecting Horses records by their ID field.