This is Hayagriva, an avatar of Vishnu. Here Hayagriva is identified by his horse head, right hand’s Vyakhyana mudra and the pustaka (manuscript) in his left hand. Hayagriva is one of the three major deities of learning. The other two are Saraswati and Dakshninamurthy.
Here Hayagriva is seated in Padmasana on an inverted lotus pedestal. The bottom portion of the Padmapeetha is beaded. As is normally the case the ornamentation is complete.
Prescribed attributes as well the the number arms differ. Though two-armed Hayagriva are known, four-armed ones are more common. The publication by Prof D Sridhar Babu on Hayagriva The Horse-heded deity in Indian culture lists two examples of two-armed Hayagriva, one dating to Pala-Sena period and one on a pillar in Varadaraja Perumal Temple, Kanchipuram.
This vigraha is from Orissa (see the peaked crown, earrings and the beaded rim) and it is about it is about 11 cm in height. The Vigraha does not show any noticeable ritual wear but the patina is deep. This may not date earlier than the nineteenth century.
Note 1: Sometimes Kalki is depicted with horse head. Kalki normally carries a sword in addition to the attributes Conch shell and Wheel. The other Hindu religious figure with a horse head is the one of the celestial musician Tumburu and he is normally shown with the musical instrument, Vina.
Note 2: Hayagriva is possibly the only deity after who a dish is named, Hayagriva Maddi prepared in Udupi region. It is a sweet dish and includes gram dal and jaggery as ingredients. Horses are fond of gram dal and hence the association.