I don't know how many koalas LA has at the moment, but I can tell you about their history. The first koalas arrived at the LA Zoo in the late 1970s. The Australia House was built for them in the early 1980s prior to the 1984 Olympics.
@Blackduiker was present when the first koalas arrived at the zoo, so maybe he can give more details of what the first koala exhibit was like.
There were koalas in the Australia House until the last one died in the late 1990s. When they got a new group of koalas from Australia it was with the understanding that they would be kept outside, so they have been in their outside exhibit for the last almost 20 years.
Yes, they are kept outside all year long, although they have indoor night quarters. For quite awhile they were not on exhibit at all after one of them got eaten by a mountain lion in 2016.