Just to add to this old post.
I work with large mosaic datasets made out of 1x1m DEM data. I've tried to use Extract by Mask to clip my mosaic for Model Builder processing. An integer raster was used as mask. The result raster was also an integer, even though source mosaic was 32-bit float.
The only feasible way, that I've found, to extract a peace of mosaic dataset, is to use the Clip raster tool (Data Management toolbox) and a polygon mask (with "Use input features for clipping geometry" on).
Quite frustratic ESRI!
Edit: Just found a simple workaround, just convert integer raster mask into a float. Still mask are generally integer, so this ads another frustrating step into my model.