If the foam seals properly between the outer skin and the rest of the structure you should not have much trouble with sweating, also take into account the conditions you will be using it is, if you will be using after the frost starts and you have a heater running inside the trailer, you "Might" have a small amount of sweating. If it were me, I would do the foam and line the floor with sheet plastic between the foam and the floor, seal the plastic around the edges with aluminum ducting tape, just make sure the foam is spread evenly so it can fill the void completely.
By the way, does this trailer have an aluminum belly skin on it? I don't remember if you already said if it did or not?
My 5th wheel has a heavy fiber impregnated belly skin on it with insulation on under the floor and aluminum skin and I use it for elk hunting, with no condensation problems during Nov and Dec and believe me, sometimes it gets really cold, but rarely do we have high humidity to create a sweat problem.. I only time I have had any sweat problems is when we went to the coast a couple of years ago.