Now these (and I have to admit the recent photos of the Old Courthouse in Toronto) are not western courthouses at all, but eastern ones, including one very old eastern one. They're posted here, however to demonstrate the appearance of eastern courthouses and how they influenced the latter ones of the West, or not.
The first is the Carlisle County Courthouse in Carlisle Pennsylvania. This Federal style courthouse strongly resembles those built by the Federal government everywhere in the 1930s. This isn't a Federal courthouse, but its style shows up in the West quite a bit.
The second is the Old Courthouse, across the street from the one above. This one is quite old, having been built in 1846, and is of another style. I've never seen this style used in the West.