starthorn

Wax will make a material (cloth of leather) water *resistant*, not water *proof*. You'll need to use something a good bit heavier and more "industrial" to make it waterproof, and even then, it may not last forever.Typically, you want to apply your water resistant substance somewhat regularly on things like shoes and boots, probably a couple of times a year, depending on how often you wear them and what kind of environment. Heavy wear or cleaning will necessitate more frequent application.Also, for leather, I'd recommend looking into specific leather protection substances. Wax will change the color and feel of leather a decent bit, and may or may not be what you want. Personally, I've had excellent experience with Leather Milk, but there are lots of options.

You could always sew an insulated material into the inside of it (many bigger fabric stores sell insulated fabric/lining specifically for things like this). It's not terribly expensive. You could sew that into the bottom 1/3 to 1/2 of the bag or something, to make it insulate better.