Is It Safe to Have Rhinoplasty when You Have the Beginning Signs of a Cold?

The temperature of 99 to 100° is a normal and safe variation of body temperature. Mild cold symptoms are not a contraindication for having rhinoplasty. As long as you do not have bronchitis, pneumonia or feeling horrible, it is acceptable to proceed with rhinoplasty.

That's a great question! Since patients' safety always comes first, I would have to say that with all the symptoms you've stated, I would avoid undergoing surgery. 
And while rhinoplasty surgery CAN be performed  in some cases where the patient manifests some lighter symptoms, in cases like the one you described, that include fever, severely runny nose and throat ache, the organisam is alreday exhausted by fighting the cold so it would be harder for you to recover. 
Another thing that's very important to keep in mind is that you should avoid taking medication that contain acetylsalicylic acid for at least a week prior to surgery since it could to some extent increase the risk of bleeding during the surgery and recovery process and a lot of cold medicine contain that active ingrediant. 
I would definitely advise you to first fully recover and that have the surgery, to avoid all possible complications!
If the stated symptoms don't pass in a week, I would also advise consulting with your general practitioner! 
Good luck!

Rhinoplasty when you are having a cold can increase your risk of complications.  There are always variables though that can increase or decrease this relative risk.  But with a cold, you can be more likely to have a cough after the procedure that could increase your risk of causing bleeding after your procedure.  Also if you are getting general anesthesia, the cold can increase your risk of having airway issues such as laryngospasm.  Most anesthesiologists will cancel a case if the person has a significant cold and with fever.