This is the case in several breeds. Were you unable to find a dog bred from hunting lines? I imagine there are not many in N. America but working cockers are hunted in the U.K. Is Lady an American Cocker or an English Cocker?
No matter her ability to withstand cold and rough conditions, you could still enter spaniel tests to get some of the feel of it with her. It's not quite the same thing but might satisfy the urge a bit?
I don't see why you can't hunt her anyway and just modify your expectations. Surely she can do bit of cold weather work if outfitted in neoprene? And not keep her out all day? Be able to dry her off in the field and have a warm place to lie down?