The goblins take them. It is supposed that they were eaten, at least that is what the narrator hinted at in the description. The last they were seen was in the great hall just before Gandalf put out the lights.
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Bilbo's ponies name was Myrtle
Before they reached Rivendale, the pony carrying their food fell into a stream. Going over the mountian, the ponies and all their belongings were taken by the goblins. In Mirkwood they ate it all.
Smaug tells Bilbo not to trust dwarves:In return for the excellent meal [of the Company's ponies] I will give you one piece of advice for your good: don't have more to do with dwarves than you can help!Smaug-The Hobbit: "Inside Information"
Gandalf tells Beorn the story of the journey from the start to the point that takes them to Beorn's house. Beorn is intrigued and entertained and so, as the group are no threat to him, he allows them to to stay in his house for the night. While they sleep, Beorn travels to discover if the tale he has been told is true. It is and as they have killed the Great Goblin (Beorn hates goblins) he agrees to give the group supplies and ponies to take them to Mirkwood.
The Stone Ponies