I would probably creosote the floor first, and maybe put down a second layer of treated wood, then the mats on top. It should mean that the lifetime of the floor is greatly extended, and the beauty of wood is that you can replace rotten boards quite easily. You could also put a plastic sheet onto first floor, put second layer of boards down, treat with creosote or similar, then cowmatting. It would also provide great insulation in winter.
But milkers do pee an awful lot....
We had our chicken houses with a single treated floor just for coming up for five years now, (and the floor does get quite damp during the wetter months) and no sign of any rot as yet.