Yes, one may workout but for shortened duration and with reduced intensity if symptoms are above the neck i.e. common cold, stuffy nose, sneezing or jaw pain.
As these symptoms are minor, one can take appropriate cold related medicines and then put in mild exercise with proper care.
Note that, light or moderate physical activity may help open up the nasal passageway, thus helping us feel better.
But, on the flip side there is a chance of spreading germs or viruses to others.
On the other hand, if the symptoms are below the neck i.e. fever, vomiting, cough, shortness of breath, etc. then one should not exercise.
Our body needs rest in this case, hence one should not overwork, as it will make it difficult to recover and may also lead to fatigue or dizziness.