why does my basement cold water pipe only rattle during cold weather?

expansion in summer, pipes tight.)

contraction in cold winter, pipes lose:(

easily solved by adding some extra hangers, for extra insurance wrap pipe with bicycle innertube, then install or reinstall hanger.

its only a real problem if the pipes are buried in a finished basement: (

No... the pipe is smaller.

Its heavier but more importantly it is colder which causes the tubing to contract which might shrink it just enough to contact something.

Everything has a natural vibration frequency. Changing physical properties of an item will change this frequency. The typical "fix" is to add additional clamps or bracing close to the source, or add a hammer arrester close to the tap. And, yes it is possible the temperature change can cause a vibration. Cooler water is slightly heavier and moves slower than water at higher temperatures.

I once owned a house from the 20's where an old Saturday Evening Post was wedged between pipes and joists to silence things a bit.

if you have basement access try holding on there while someone tries to create noise.

may be possible to push on lines to stop noise, most easily tried by using your hands and pushing pulling etc on lines

It's called "shivering," and is a normal physiological reaction to extreme cold.