In Ramayana, hanuman speaks chaste Sanskrit to Sita. Jambavan, jatayu et al are also able to talk. As far as I know this is a post-rigvedic development. An Indo-European parallel is Hector's horse talking to him in the Iliad.
As for as I know, animals are depicted as talking in Rig Veda at some occasions but only in Mandala 10. In Rig Veda, 10.108 Sarama, the celestial bitch and messenger of Lord Indra, talked with Panis.
- WHAT wish of Saramā hath brought her hither? The path leads far away to distant places. What charge hast thou for us? Where turns thy journey? How hast thou made thy way o’er Rasā's waters.
2 I come appointed messenger of Indra, seeking your ample stores of wealth, O Paṇis. This hath preserved me from the fear of crossing: thus have I made my way o’er Rasā's waters.
Rig Veda also mention Vrishakapi, the ape friend of Lord Indra at some places like RV 10.86. Also the twin Ashvins have lot of Suktas dedicated who are said to have horse head.