Thanks for your question.
Pregnant women may also have cough
& cold like normal people. Generally it has no known adverse effect at this stage of pregnancy
unless you are having high grade fever
However many infectious diseases present as cough & cold in the start, so, if it do not settle within a couple of days, you develop any rash
or you have a history of contact with someone with a known infectious disease you must report this to your treating obstetrician for expert opinion.
Wish you best of luck