I spent 4 months down in the Falklands in late 86 early 87, and there were literally no trees at all, I was based out of Fox Bay on West Falkland Islands, and it was bleak and barren, I don't recall ever seeing any trees on West Falklands including Saunders, and Pebble Island, if my memory serves me correct, there was a tiny patch of trees just outside Port Stanley, near Murrel River.
It was a a bleak miserable place to be, despite it being their Summer, you could easily get 4 seasons in one day!!
The Mountains were pretty spectacular though, especially Mount Alice, where the RAF Phantoms of 23 Squadron would have regular "Track Ex" simulated attacks, designed to test the Rapier Batteries protecting the AEW "Golf Balls" which had long been removed, but the Phantoms used to fly as low as they could over the golf balls, so that the shock wave would send shit flying all over the place inside the accommodation up there...
Wildlife was spectacular, the local inhabitants were not however.
South Georgia wasn't much better..
Trees would be totally inaccurate for the 1982 conflict.