How would you make a cake with condensed milk? And how would that cake taste? Can you mix the milk into the batter??

I have not done this, but you could probably substitute the liquid with the condensed milk. Since it is sweetened, it would make the cake sweeter. Here in Tucson, there is a tres leches cake that is made with the condensed milk and two other cremes poured over the cake after it is cooked and cooled.

Its a very rich wet cake. Then its iced and refrigerated.

I haven't done this either, but I would think you would have to be very careful with the recipe. Since condensed milk is very thick and sweet, the flavor and texture would be effected if you tried to tweak your regular cake recipe. Most of the recipes I've found calls for pouring it over an already baked cake, except for this one for condensed milk pound cake:
http://simplyannes.blogspot.com/2008/02/afternoon-delight.html

-Rezzy