Clipless pedals really don't keep your feet any warmer, they suck heat out through the metal cleat.
In very cold weather you need a shoe with a looser fit. Mesh shoes have obvious drawbacks. I just use basic athletic shoe with a non-mesh upper. Some carry a lot of foam which can soak up water in the wet. Winter cycling shoes and boots often use Lorica synthetic leather. A leather sports shoe will be fine in the dry but can soak up water.

A 2-sock system should be fine but I prefer thin woollen socks as an inner layer. They can be fancy merino or just plain everyday ones. You can also get waterproof socks such as Sealkinz which are good in the cold.