This is Hayagriva, an incarnation of Vishnu. Hayagriva, with horse head, is one of the three major deities of learning and the other two are Saraswati and Dakshninamurthy.
Here Hayagriva is seated in Padmasana. His lower right hand is in cin mudra, expounding knowledge gesture. He is holding Shankha, Chakra and Pustaka is his hands, starting from upper right hand clockwise. It is the cin mudra and pustaka identify Hayagriva as a deity of learning. Prescribed attributes of Hayagriva differs. More about it later.
One of the interesting aspect is the provision of a single hole to support the Prabhavali. See the back view. Hayagriva is one of the few deities to have Chandra Prabha (Circular prabhavali) and hence the arrangement. (Thanks to Jainam for this information). However this arrangement is not always followed.
The picture below shows three of the Hayagrivas in my collection. It is the placement of Akshamala or the absence of Akshamala that makes it interesting. Starting from our left, Akshamala is held on his left upper hand. In the middle one Akshamala is held in the lower right hand, the one with cin mudra. The rightmost one, the subject of this blog, Akshamala is absent. The Akshamala was introduced after Madhvacharya.
Even today there are followers who distinguish between the two, Madhwa (with Akshamala) and non-Madhwa (without Akshamala), while acquiring the Vigraha for worship. These minor traditions make life interesting.
This Vigraha is most likely from North Karnataka. It is about 7 cm in height. The Vigraha shows significant ritual wear. This may not date earlier than the seventeenth century.