In a book on color published by the National Gallery in London, David Bomford (Associate Director for Collections at the J Paul Gerry museum in Los Angeles) and Ashok Roy (director of Scientific Research at the National Gallery in London) write: "...by early Renaissance times professional supplies of pigments existed ... Prepared oil paints were kept in the studio under water to prevent them from drying out."2
Of course traditional use doesn't always match modern scientific knowledge. Asked about submerging oil paint under water, Anne Marie said:"Exposing an oil painting to water or high humidity is damaging because it can disrupt the cross-linking of polymers, leading to a loss of adhesion (which is naturally poor because linseed oil is not a strong adhesive).
"I would not recommend storing paint or a palette under water, since high humidity inhibits polymer cross-linking, weakening the paint. If the paint is sealed, this serves no purpose except perhaps to prevent rapid temperature swings. If the paint is not sealed, the high humidity can be damaging. Exposure to alkaline conditions may also increase the degree of yellowing over that which would naturally occur."
And to quote from Just Paint again: "There are also chemical reactions that can break the polymer chains in oils. The most common is chemical reaction with water. This reaction is usually slow, but it gets much faster if the paint film is exposed to humid air under alkaline conditions. This becomes a problem if the paint is formulated with alkaline pigments or if it is applied over an alkaline surface."1
So although there's anecdotal evidence from oil painters who've put their oil paints under water and not seen any issues, and it's a practice with a long tradition, it isn't sound on a chemical level. But freezing oil paints, that's fine if you've a large enough freezer. Personally, I think I'll stick to using my freezer for ice cream.