Some colds are viral, others are wind-cold or wind-heat colds.
Pay attention to rest when you have a cold. If it is viral, people who catch a cold and don't pay attention to rest may cause very serious consequences such as viral myocarditis.
Therefore, if you have a cold, you should drink more water, rest more and eat lightly.
Of course, if you have a slight cold, you are in good health. Then you can exercise properly.
However, personally, this is not recommended!
I'm happy to answer your question. I wish you a speedy recovery from your cold.