In their cases if they have cases. In holster if they have holster and no box.
If I come from the range, I keep them under open air at home for some time to ensure they dry out (see note below for winter) and then put them to storage.
The bottom of my safe has a pile of silica packets, e.g. wife buys new shoes, package has silica packets, packets go info safe.
So far, no rust or hint of it.
PS.
Soaked foam or cloth in oil makes no sense. It does nothing. Take the wet gun, wrap it in oil soaked anything and it will rust.
You have to control humidity. Since it's a winter time, you have to remember that your gun will be cold and if you place it in warm environment, the water in the air will end up on your gun. You may want to keep your gun in the case for a while so it would warm up slowly, then you have to dry it up just in case (including its box and foam in the box). After it dried up, you can clean and oil it and then put it for storage.