| Registered Name | Owner / Club | Status |
|---|---|---|
| Happy Gilmore | Liisa Rantamaki Rathangan | Approved |
| Happy Harry | Geraldine Bellew Border Counties | Approved |
| Hard To Hold | Louise McEnteggart Boyneside | Approved |
| Hardingville Delaware | Deirdre Connolly North Cork | Approved |
| Hardingville For Suir | Deirdre Connolly North Cork | Approved |
| Hardingville Haze | Deirdre Connolly North Cork | Approved |
| Harghano | Victoria Tynan Kerry | Approved |
| Haribo | Alison Curtis Thornton | Approved |
| Harlequin Beauty | Clodagh Burke Warrington | Approved |
| Harlequin Du Clover | Claire Solon Kilronan | Approved |
| Harlequin Grey | Lorraine McElroy Golden Grove | Approved |
| Harlequin Moment | Emily Vial Clonshire | Approved |
| Harley Irl | Fiona Kavanagh Clonough | Approved |
| Harley Quin | Peter Dargan Kilrainy | Approved |
| Harmon Yeats | Muireann O'Toole Brennan Tinahely | Approved |