In Oregon the snow level at the beginning of May and the end of May are different enough that it is hard to generalize about the whole month.

I can tell you that the weather last winter was unusually wet. In the six months since October 1st the Portland area received about 4 inches more rain than it normally gets in a whole year (40" vs. 36"). However, the winter was somewhat warmer than average, so that below 4000' almost all that fell as rain, not snow. Above 6000' almost all of that fell as snow, so the upper elevations are buried and the mid-elevations can be rather bare. Except this pattern of snow distribution varies locally, so you really need good information about local conditions.

A great place to pick up such local information would be:

http://www.oregonhikers.org/forum/

Visit there about two weeks before you plan to go and you can probably pick up some knowledgeable advice.