Try:
=IF(OR(COUNTIF(Sheet1!$E$2:$E$300,A1),COUNTIF(Sheet1!$G$2:$G$300,A1),COUNTIF(Sheet1!$I$2:$I$300,A1)),"Present","Not Present")
or probably even, just:
=IF(COUNTIF(Sheet1!$E$2:$I$300,A1),"Present","Not Present")
If the columns between won't contain the horse's name anyways....