Engadin is an extremely beautiful valley in south eastern Switzerland. The main and most of famous city is St. Moritz a posh holiday place for rich people; though the beauty of the mountains the silence and the fresh air shouldn't discourage a hitchhiker to try his/her luck there.
Hitchin in and out
The main accesses are from Chur (Julierpass from Vaz or Thuses, motorway to Lugano) or Davos from North and from Val Bregaglia and Chiavenna Italy from south (Malojapass). Rather you may think that is a posh place where nobody will pick you up, there are lots of nice locals and workers who pass by these roads and you won't have big difficulties finding a lift even though the spots are not very perfect (often no space for cars to pull over). Especially during the weekend you can find quite long distances lifts, e.g to Lecco or Milano
Accommodation and Sleep
In summer you can find wild camping spots everywhere outside of the towns, as any other mountain place. Though in winter Engadin can be really cold with an average of -15, -20° C. The air is really dry so you don't feel it very strong but still is -20..If you don't have a proper gear, ask some farmer to sleep in their barns or search some house undercostruction (in Sils-Maria December 2013 there was one open and heated right in the centre..) where you can hide and not freeze.