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

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!

The answer is: maybe. If a patient is running a fever (>101°F), has chest congestion, or has sinusitis, it's probably best to delay surgery. Sinusitis--at least in theory--could infect the nasal soft tissues (though I've never seen or heard of this). Congestion or fever post-op could be mistakenly attributed to congestion and fever pre-op, and thus a more serious complication could be missed.

It's best that the surgeon and the anesthesiologist evaluate the patient under such circumstances to see whether it's reasonable to proceed.

All the best,

--DCP

I ask my patients to let me know if they get a cold before proceeding with Rhinoplasty Surgery. I feel it's best to operate on your nose when there is no infection or congestion. This may just be nasal allergy which can often be treated before your surgery. You should visit your surgeon for an examination and specific advice.

I hope this is helpful for you.