Race Horse Cost Recovery Act of 2023 This bill amends the Internal Revenue Code to modify the accelerated depreciation allowance for race horses to allow a three-year recovery period for any race horse. (Current law limits the three-year recovery period to race horses placed in service before January 1, 2022, and race horses placed in service after December 31, 2021, that are more than two years old at the time they are placed in service.)