The short answer
A heater that blows cold air usually means hot coolant is not reaching the heater core. The cheapest cause is low coolant, then a thermostat stuck open, a blend door that will not move, air trapped in the system, or a heater core clogged with sediment. If the temperature gauge never reaches normal, start with the thermostat.
How the heater works in the first place
Your car’s heater is a small radiator, the heater core, that sits behind the dash. Hot engine coolant flows through it and the blower pushes cabin air across it. If the coolant is not hot, is not reaching the core, or the air is being routed around the core, you get cold air. Everything below is one of those three problems.
Low coolant
The heater core is often the highest point in the system, so when the coolant level drops it is the first thing to run dry. Cold air that comes and goes, especially on corners or hills, is a classic sign. Check the overflow tank when the engine is cold. If it is low, the next question is where the coolant went: a leak, a weeping water pump, or something more serious.
Thermostat stuck open
If the temperature gauge takes forever to climb, or never reaches the middle on the highway at −25°C, the thermostat is probably stuck open and the engine is not warming up. You get lukewarm air, worse fuel economy and extra engine wear. It is a relatively inexpensive repair and very common on older vehicles.
Heater only cold at idle, warm when driving
Warm air on the move and cold air at a red light usually points to low coolant or a water pump that is not circulating enough at low revs. Air trapped in the system after a recent coolant job behaves the same way. Both are worth a look soon, because the same conditions can lead to overheating in summer.
Blend door and controls
Modern cars route air with motorised doors inside the dash. If a door actuator fails, the heater can be stuck on cold on one side, or clicking behind the dash when you change temperature. The engine and coolant are fine; the air is simply not being sent through the core. Diagnosis is by scan tool and listening, and the fix can be a small part in a hard-to-reach place.
Clogged heater core
On a car that has gone years without a coolant change, sediment and rust can block the core. Both heater hoses hot but the air still cold is the tell. Sometimes a flush clears it; sometimes the core has to be replaced, which is a bigger job because it means pulling the dash. A sweet smell in the cabin or a fogging windshield that will not clear means the core is leaking, and that needs attention quickly.
Why not just live with it
In Winnipeg, a dead heater is a safety issue, not a comfort issue. Without heat the defroster cannot keep the windshield clear, and several of the causes above are early signs of cooling problems that get expensive if ignored. Garage 46 diagnoses the actual cause, pressure tests the system and quotes the fix before any work.