Why is the Horn written without key signature here (4 sharps)?
Transposed? (In La=A)
The OP is referring to the Horn (Corno) not the Clarinet.
Horn parts are generally written without a key signature, a practice stemming from the time when they were not chromatic instruments (in other words, before valves were invented).
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Oooops sorry @rkrentzman and @wcreed, I spot the first… 
The true answer is that above:
Thanks!
Just to visualise: Natural Horns (Horns without valves) did have different crooks for each key, which they would have to switch before playing and also in between different sections.
Horn in Fa would mean for the Hornplayer to attach the crook for that key.
They did have a few crooks in chromatic order, like Horn in F (Fa), Horn in E, Horn in E-flat, Horn in D…
Also Horn in A or A-alto, or Horn in G and G-alto.
In German they would call the crook a Bogen - a brass tube of a certain length.
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