The distinction that decides the claim is sudden versus gradual. A pipe that fails all at once is covered. A pipe that leaked slowly behind a wall for months is usually denied, because insurers treat long-term seepage as a maintenance problem you were expected to catch.
Frozen pipes add a wrinkle: many policies cover the resulting water damage only if you took reasonable care to keep the home heated. Leaving the heat off in a vacant house during a freeze can jeopardize the claim.
Either way, document the burst and the damage immediately and start mitigation - most policies require you to take reasonable steps to prevent further damage, and waiting can both grow the loss and weaken the claim.