The use of sawdust, wood chips and shavings is not recommended not just because they are dusty and stick to everything, but also because they harbor pathogens, specifically psuedomonas, that has the very real risk of causing a problem, especially when one considers you're dealing with an animal born with no immune system initially and open entry sites for those pathogens (navel, nose, mouth, etc.). So, hay as ryu recommended is a logical alternative. We can get chopped up cardboard boxes here that work really well - better than I anticipated.
Hope that helps.
Kathy St.Martin
Equine Reproduction Short Courses
Equine Reproduction