How does the scene outside the window foreshadow the feelings that sweep over Mrs. Mallard as she sits in her chair?

There is so much foreshadowing in the description of what Mrs. Mallard sees outside her window:

She could see in the open square before her house the tops of trees that were all aquiver with the new spring life. The delicious breath of rain was in the air. In the street below a peddler was crying his wares. The notes of a distant song which someone was singing reached her faintly, and countless sparrows were twittering in the eaves (para. 5). 

There were patches of blue sky showing here and there through the clouds that had met and piled one above the other in the west facing her window (para. 6). 

In addition to the foreshadowing explained in the other responses, there are the sounds of the sparrows Mrs. Mallard hears, birds that are free to fly, while she has been a bird in a cage in her marriage. The "open square" is a reference to the open life she believes she can now have, and the clearing of the sky symbolizes how the clouds in her own life, i.e., her marriage, are now cleared away, or so she believes. Mrs. Mallard sees how she can now sing in happiness, like the birds or like the distant singer she hears below. And she can also smell the rain, which symbolizes not only spring and new life, but also cleansing, a way of cleansing herself from what was clearly an unhappy marriage.  

This is a wonderful use of foreshadowing, not only because of its careful choices of words that presage Mrs. Mallard's fleeting hope for freedom and new life, but also because of its vivid imagery.  Chopin appeals to the reader's sense of sight, smell, and sound in these passages, providing a fuller image of new life and freedom than just visual imagery would have accomplished.