What document must be filed to determine entry date preferences for horses?

The document that must be filed to determine entry date preferences for horses is the preference date application. This application is specifically designed to inform racing officials about the horse's racing history and entry preferences, allowing them to allocate entry dates accordingly. It provides vital information that helps ensure a fair and organized process in determining which horses can enter races based on their eligibility and prior performances.

While the other documents mentioned have their purposes, they do not serve specifically to determine entry preferences. The owner's contract pertains to the relationship between the horse owner and trainer, foal certificate papers validate the horse's identity and lineage, and a claim form is used when a horse is being claimed in a race. However, none of these documents address the criteria for entry date preferences, making the preference date application the correct choice.