Is it okay to apply a cold compress when my face looks swollen in the morning?

Every morning, the area around my eyes and cheeks looks a little puffy, so it bothers me a bit.
It seems to be even more so on days when I ate late the night before or didn't get enough sleep.
In times like this, applying a cold pack for a short while does seem to reduce the swelling.
However, it is recommended to avoid applying ice directly to the skin, as it can be irritating.
It is said that doing it briefly in small amounts is fine, using a method that is gentle on the skin, such as with a chilled towel.
I am also trying to cut down on salty foods and late-night snacks before going to sleep.
I'm curious what method was most effective for everyone when managing morning swelling.