Working out while sick

Is there anything wrong with working out while sick? I've had a cold for the past week now, mainly my throat is very dry and I have a bad cough.

But I don't want to miss my workouts! So I've been doing them, the only thing is since my throat is already sore breathing heavy is hard and it just makes it a little drier.

Is there technically anything bad about working out while sick or is this okay as long as you can handle it?