During and prior to Harry's years at Hogwarts, Hagrid probably stayed at Hogwarts with the students, as he doesn't have many friends and most of his family are dead, except for Grawp. The first time Hagrid and Madame Maxime met was in GoF, so he might have stayed at her house in Harry's fifth or sixth year, too. I like to think Hagrid had his own happy epilogue, in which he and Madame Maxime get married. After DH, he would be welcomed at the Potters and Weasleys. Maybe he stayed over at Dumbledore's or on a staff retreat.
How do you think Hagrid spends his Christmas'? Does he just stay at the school with the students, or do you believe he does to stay with friends (Madam Maxime, perhapes?)? Do you think after DH, he might be invited to have Christmas with the Potters and the Weasleys? Or does anyone else have any other ideas?