Did you remember to remove your garden hose from the faucet last fall? If not, the residual water in the hose caused the faucet to freeze and split open. Always remove your hose from the faucet before freezing weather arrives in the fall.
During extremely cold weather the intake pipe on a high-efficiency furnace can frost over and this can cause the furnace to quit. Carefully remove the frost from the intake pipe. Also, a long icicle can form on the exhaust pipe and that should be carefully removed as well.
Most homes have a main shut-off located near the water meter in the house. Newer homes have a ball valve with a handle that turns 45 degrees/perpendicular to the water line to turn the flow off. Older homes have a round valve that is turned clockwise to turn off the flow of water. Sometimes these old valves are immovable so it is NOT recommended that you apply too much force to one that is stuck.