Mormonism and temples/Do temples always face east
Do Mormon temples always face east?
Do LDS temples always face east?
Temples face whatever direction is most practical and artistically pleasing for the site they are on.
The front of the temple is the elevation where the phrase "House of the Lord" is found. So, for example, the "front" of the Provo temple is on the east-northeast elevation as the temple itself is 20 degrees off of a true east/west axis. The front of the Oakland Temple is the north elevation, and the front of the Los Angeles Temple is the southeast elevation. The Stockholm Temple faces due south, which, at such a northern latitude, would be the direction of the most light; its front is, therefore, the south elevation.
Nauvoo is an interesting case as it has the phrase on both the east and west elevations of the building. We know that the original Nauvoo temple had the phrase on the west elevation but no photographic record or architectural drawings exist of the east elevation, so the design of the east elevation of the modern Nauvoo Temple is guesswork. Thus, in the case of Nauvoo, you can take your pick on the west or the east elevation as the "front". Most people, however, would say that the west elevation is the front of the building as there are no doors on the east elevation.
In summary, to find the "front" of an LDS temple you find the phrase "House of the Lord" on the building itself, not on a sign. The elevation that the phrase is on is the front of the building. It is not always the east elevation. The angel Moroni statue has nothing to do with what is the front of the building. Temples are placed on the site in the manner that is most practical and artistically pleasing for that particular site. They can face in any direction.