Yes, the White House was set alight by the British Army but not during the War of Independence.
The White House didn't exist during the American War of Independence (1776ish). They didn't have an elected President until 1789 (G Washington) and the White House wasn't liveable until after he'd retired. The second President, John Adams moved in in c1800. He'd taken over from Washington in 1797.
I'm not certain that the building had been completely finished off when it was burned by the British Army in 1814, during the War of 1812. The original building was just the central portion of what's there today, i.e. no East or West wings. The troops who participated in the raid didn't march from Canada, they were brought in by the Navy from Chesapeake Bay. I don't know if the Guards were involved but certainly marines were involved in the action.