Based on what I gather from your situation I would put the money and effort from the drain tile and put it towards landscaping as a solution.
It sounds like you have the ability to slope the property away from the barn. That is the best long term solution, as with anything, mother nature always will win and all drain tile (or anything manmade) will eventually be rendered useless. Further, with clay soil a perf. drain pipe will only serve as a collector drain for surface water (shallow trench with stone up to the surface, or maybe a little topsoil over it). You would have to grade the area towards this type of drain anyway. A drain tile really is meant to 'absorb' water from its surrounding area (like a reverse septic field). Clay won't let the water move.
You did mention putting down a concrete slab at some point. If you do, place it over clean stone. Then you run a perf. drain along the outside perimeter about 8" below grade and continue the clean stone into that trench. Then, any water or moisture that comes up from below will flow through the stone to the drain keeping moisture away from slab. No freeze/thaw cracking.