It is Aarne-Thompson type 531.
A royal huntsman found a feather of the Firebird and, though his horse warned him against it, picked it up. The king demanded that he bring him the bird. The huntsman went to his horse, who told him to demand that measures of corn be spread over the fields. He did, and the Firebird came to eat and was caught. He brought it to the king, who said that because he had done that, now he must bring him Princess Vasilisa to be his bride. The horse had him demand food and drink for the journey, and a tent with a golden top. With it, they set out to a lake where the princess was rowing. He set up the tent and set out the food. The princess came and ate, and drinking foreign wine, she became drunk and slept. He carried her off.
Princess Vasilisa refused to marry without her wedding gown, from the bottom of the sea. The king sent the huntsman for it. He rode the horse to the sea, where the horse found a great crab and threatened to crush it. The crab asked the horse to spare it and summoned all the crabs to fetch the wedding gown.
Princess Vasilisa refused to marry without the king ordering the huntsman to bathe in boiling water. The huntsman went to his horse, who charmed his body. He bathed in the boiling water and became handsome. The king went to bathe in the same water, and died. The people took the huntsman as king instead, and he married the princess.