I'm not sure if there is a hostel at STANTON but one cheap option I know of is to get a group together and rent an appartment in St. Jacob--the next town east of STANTON and accessible to STANTON lifts via the free shuttle bus system.
Anyway, if you really want to save money, you might consider a less expensive resort. Soelden, while certainly not the cheapest place in Austria by a longshot, has a lot of affordable accomodations very near the lifts. Soelden does not have as many kilometers of skiing as the Arlberg writ large but it is bigger than the Galzig and Nasserien areas of Stanton combined. It also has a lot more terrain over the 2600 meter mark, including two glaciers. In short, you'll be able to bag some nice, big mountain decents if that's what you into. If you are into off-piste, STANTON rules but there's respectable off-piste at Soelden if you know where to look.
For more on Soelden, check out this article I wrote:http://www.dcski.com/news/2004/02_16_2004/europe.php3