

The reason the bodies are preserved so well is because of peat that is present in the marshes. Peat is formed by the buildup of organic particles which makes it rich in minerals and fertile. This helps keep the bodies look like they are recently deceased when in reality they could be months old.
Shire is located in the north west region of middle earth and is home to the Hobbits. Shire is a transport limited landscape. This means that the heavy amount of vegetation (in this case grass) limits the rate at which erosion can happen. This makes Shire an ideal place for Hobbits to live in peace. Also, since the houses are underground, they are very well insulated.
Images cited:
http://images.wikia.com/lotr/images/4/48/Dead_Ones.png
http://scrapbook.theonering.net/scrapbook/group/911/view/7730
http://www.exploring.co.nz/static/images/7/117-hobbit-holes-hobbiton.jpg