I found a set of snow tires with wheels that are 185/70/r13 . With these work with my 07 Fit?

 

On my GE8 (2010), 14-inch Civic alloy rims are pretty tight on the front, so unless your 2008 has significantly smaller diameter brake rotors I don't think a 13-inch rim will clear the front brake calipers.
But, when in doubt, it only takes a couple minutes to see if they fit.