if the engine doesn´t starts, check the air filter, the distribution cap and rotator, the cables to the sparkplugs an the spark plugs. When you turn the key, but doesn´t start, you should hear a low humming noise from the back of the car, that stops after 2-3 seconds. That was the main fuel pump, building up pressure in the fuel lines. If that was all ok, we have a litte problem.
If you have an engine with a central injection (SPI) in the throttle body, try the following steps. When you take out the air filter you can look into the throttle body if its messed with layer of a black oil-coal mixture, clean that throttle body. Your car has a cold-start-system, if the temperature is under a certain temperature an extra channel in the throttle body is opened up to have a richer mixture, wich helps to start at low temperatures. When this channel is closed by the oil-coal mixture you have issues.
A problem with the vacuum system could be found rather easy, when the engine is running. open a connection in the vacuum system and hear if the rev. changes, it should change, now close both ends, one after the other with you thumb, hear if something changes. Then put the connection back togehter then open the next one until you find a connection where the rev. doesnt change until you close the line with your thumb. An indicator for a working vacuum system is the small red pimpel on your thumb while closing the vacuum line.
If you have an engine with a injection valve for every cylinder (MPI) i would guess that the engine gets "false air" by a leak in the air intake system. The mass of air is meassured and the black box already calculated the matching ammount of fuel. If the engine gets more air, than calculated, by a leak in the air intake system, the mixture gets lean an the engine doesn´t start well when its cold.
Start up the engine and buy a can of a.e. break-disk-cleaner, now spray, only 0,5 seconds per spray, the air intake in smal steps beginning from the air filter to the throttle body. Spray listen if you hear that the rev. goes higher, no next spot until you hear the rev go higher than you have found your leak.