Aside from inspirations from the [Kalevala][1] and Beowulf, Tolkien had many sources of inspiration.  Tolkien himself admitted to borrowing ideas and bits and pieces from other epics, legends and tales.  Many of the best author's do this and you can see similar influences in J.K. Rowling's work and C.S. Lewis' works as well.  Even the Legend of King Arthur itself has echos similar to viking legends AND the story even echos that of the  Christ as Arthur is expected to return when he is needed again.  In Tolkien's books and others, to truly get the most out of the symbolism, it is helpful to know at least some of the source inspirations. 

Tolkien, does reference Arthurian Legend - Aragorn is a dead ringer in many ways to the legendary King Arthur himself.  The hunt for the White Stag is one example of these kinds of references.  In the Arthur Legends the White Hart often is a portent of one of the knights having crossed a forbidden boundary (as the hobbit and dwarves have just done in crossing the river into the elven king's territory).  It also often appears before a change in circumstances or just before a new adventure ensues (which you can certainly say happens forthwith in The Hobbit as well).

Lastly, to many cultures of the Classical and Medieval age, the deer represents life or a power that is life-giving.  The group stumbles across the deer when they are in the most need of a little hope as they are hungry and down trodden at this point in their journey.  Tolkien is probably capitalizing on this association as well here to tell the reader that a hunt is occurring nearby and hope will arrive. 

For an essay on signs of Arthurian Reference in LoTR [click here][2]
For more information on the symbolism of the white hart or white stag in mythology [click here.][3]


  [1]: http://news.nationalgeographic.com/news/2001/12/1219_tolkienroots.html
  [2]: http://www.scribd.com/doc/19165420/Arthur-and-Aragorn-Arthurian-Influence-in-LOTR
  [3]: http://www.maryjones.us/jce/whitestag.html