| As already mentioned, most colds commonly take a couple days to incubate.
In fact exercise is a good thing to do when you're incubating a cold because it helps your body fight it as long as you don't overdo it. Remember that metabolism is an accumulation of ALL reactions in your body, this includes your immune system which gets stronger through exercise, and gets a boost during exercise.
And yes, colds are NOT caught by being cold. This is an old myth. Colds are caught through bacteria in the air, in cold weather our immune system is lowered, and thus we're more likely to contract the sickness. I seem to remember hearing something about the cold air helping the bacteria survive as well, but I don't know.
If anything my guess would be that the sudden urge to start a regular exercise could have been your body's way of responding to fight off the cold while it was still incubating.
Keep exercising while you're sick, just reduce it and don't push yourself at all. If you can take it easy and still stay as active as you can manage, the cold should clear up much faster.  | 
