Yes, the cold can cause the eyes to swell because of the decreasing immune system. At this time when you get cold, you will find that you may easily get the bacterium in your eyes. That is the main reason to cause the swelling eyes. You should drink more water and use some medicine to get rid of this.
Yes a cold in deed will make your eyes appear swelling. Several things can cause inflammation around the eyes, including a lack of sleep, or an infection like pink eye (which can be a viral or bacterial conjunctivitis). Allergic reactions can also cause swelling of the eyes. There exist several low-cost home remedies for swollen eyes, which are worth trying before turning to over-the-counter remedies.
Just like Hot Compress, Cold Compress, or you can use Cucumber or tea bag.
This kind of phenomenon is very common, because the eyes are sensitive with the fever, so you do not need to worry about it. Once your cold has gone, your eyes would be OK. If you do not like the swelling eyes, you can deal them with cold compress, but overall you should pay main attention on your cold, which is the basic reason of the swelling eyes.