1) Probably a diminutive of Robert via the pet forms Rob, Hob, but used of a middle-sized horse.
1257 et j equum album qui vocatur Hobbe, Harpham. The diminutive is said to have referred originally to horses from Ireland but that connection is not obvious in Yorkshire examples from the fifteenth century: 1420 I will that Sir Robert Shottesbroke ... haue the sorde hors and litill Hans the hoby, York
1487 I shuld knowe this horse ... for I trowe that he was my Lorde of Lincolne hobye, York
1568 one yonge dapled grey hobby, Lupset
1619 cosen Richard Cholmeley’s little pretty baye hobby, Brandsby.