Thanks, but unless I'm misunderstsnding (always a possibility), what I was looking for was a count of the points in each classification, not the number of cells. Similar to a Select by Location if the raster classifications were polygons. That's essentially what I ended up doing once the Spatial Analyst license was released. Converted the floating point raster to integer using the Raster Calculator, converted that to polygons, merged all polygons for each classification, did a Select by Location on each class to get the count.
There's probably an easier way, because that seems kind of Rube Goldbergish, but it worked.