The most common causes of a car heater blowing cold air is a clogged heater core, air in the coolant system or even a stuck thermostat.
Your car uses the engines hot coolant that passes through the heater core to produce the hot air from your cars heater vents.
If the coolant cannot flow through the heater core or your engine can't get the coolant to a high enough temperature due to a stuck engine coolant thermostat then the heater may not work.
When it's cold outside your car heater should begin to heat up after 2 to 5 minutes of the engine running even at idle.
In the winter I will allow my engine to run and warm up for 5 minutes while I'm scraping the ice off the windshield if there is any.
Then within 5 minutes the heater is working enough to keep me warm and after 10 minutes the heater is nice and hot as I drive down the road.
So your temperature gauge should start going up after a few minutes and then after 5 minutes or so the heater in your vehicle should start throwing out nice and warm or hot heat.
The heater in your vehicle uses the engines hot coolant to blow hot air through the cars heater vents.
So you're staying warm from the hot coolant in your car.
The hot coolant passes through the heater core where the blower motor blows over the heater core and produces heat.
If you're not getting heat then your heater core could be plugged up or you have a bad thermostat in the engine or your coolant level is too low.