1. He is active.
2. He is being active.
What is the difference between them?
#2 means he seems to be active at the moment, but he is not active in general or actually? Is may explanation correct?
3. He feels cold.
4. He feels being cold.
Does #4 mean he seems to feel cold, but actually he is strong and doesn't feel cold generally? Is my explanation correct?
You're absolutely right about the first explanation.
"He feels being cold" is not standard English.