No, Hogsmeade is not a part of Hogwarts. It was a separate village very close to Hogwarts Castle. However, for the purpose of jurisdiction, it was taken for granted that Hogwarts was a part of the Hogsmeade village, even though the village was a bit far from the castle and the castle rested atop the rocky highlands away from the village of Hogsmeade. Hogsmeade although not related in any specific manner to Hogwarts, was heavily influenced by Hogwarts as several students and staff visited there and visitors to Hogwarts ended up staying in the inns at Hogsmeade.