You're going to have some wires involved with a wireless repeater, but you could armor or encase them.

I'd look at a wireless repeater then. And probably a directional antenna on each side of the long link, if you want reliable operation in inclement weather. You can probably house both antennae inside the house and barn if they are highly directional.

Be careful when comparing the "gain" figures. Of course there is no real gain to be had with an antenna. The gain comes from sending the signal to a subset of sphere. Even a vertical antenna can exhibit this gain, but it's still sending and receiving to and from directions where you have no interest, and will thus generate more noise in the receiver. A yagi or dish arrangement will work the best. A dish will have a larger "footprint" for the signal, but it is only in one direction. While a yagi looks like it points at the footprint, the footprint is actually evenly split between the front and back of the antenna.