 Letrozole is an aromatase inhibitor that is approved in the first-line treatment of postmenopausal women with hormone receptor-positive or hormone receptor unknown locally advanced or metastatic breast cancer. Sorafenib may stop the growth of tumor cells by blocking blood flow to the tumor and by blocking some of the enzymes needed for cell growth. This phase III trial is studying the side effects and best dose of sorafenib when given in combination with letrozole and to see how well they work in treating postmenopausal women with metastatic breast cancer. 