There are a number of ways to record horse services, however the most common is by recording a Procedure.
There are a number of procedures that may be recorded against a horse, though not all Procedures have a cost associated with them.
To record a Procedure against a horse in Ardex;
Click Procedures in the lower-left
The Procedures window will open
Choose a date  for the procedure
Select the horse  (by name)
Select a Procedure  from the drop-down list
Once the Horse and Procedure have been selected, you can enter further information, including chargeable rates that will be attributed to the horse, and hence payable by the owner/s.
Other ways of recording transactions against horses is;
Transactions in the Finance section of Ardex
By a Group Add in Finance
For more information on Transactions via horse procedures see the Ardex User Guide - Recording Horse Procedures in Ardex (pg. 4 - Entering Horse Transactions)