I am not a horn player, but I do have a bit of knowledge about them. Horn parts can be written in the G or F clefs, right? Is it common practice to put the first horn stave (horns 1 and 3) in the G clef and the second stave (2 and 4) in the F clef at the same time? Or is it courtesy to put both in the same clef?
Bob has a lot of good information in his answer. I'll just add abit more here.
As I'm sure you know (but I'll repeat for the sake of others, and for clarity), horn players tend to specialize in either higher parts or lower parts. They are typically notated with one "high" horn and one "low" horn per staff. So you usually have:
In fact, it is not at all uncommon for staff 1 to have a high and a low part, and staff 2 to have the exact same high and low part. To me, this seems sort of the opposite of what you'd expect, but it is what it is. As a result of this layout, you might expect that when one staff switches to bass clef (which is pretty rare), it is the low horn that will mostly be playing that part, and the high horn on that staff might not even be playing.
I just flipped through my entire score of Holst's The Planets and found only one instance of horns using the bass clef. It's on the first two pages of Mars, when the main theme is first heard. Holst is using a larger orchestra, with 6 horns, and he has them divided into two staves of 3 horns each: staff 1 has horns I, II, and III, while staff 2 has horns IV, V, and VI. In this passage, the second staff switches to bass clef, and only horns V and VI are instructed to play, in unison (horn IV presumably specializing in higher notes, and not needed to balance with the rest of the orchestra). Technically, staff 1 is still notated in the treble clef at this point, but none of those horns (I, II, III) are actually playing anything here, so its sort of a moot point.
Looking at Norman DelMar's Anatomy of the Orchestra, he discusses the alternate possibility of combining the high horns (I and III) on one staff, and the low horns (II and IV) on another staff. Of this he says:
The example he uses to illustrate this point is from Bartok's Dance Suite (bars 90-96), in which I and III are on a staff in the treble clef, and II and IV are on a staff in the bass clef. Unfortunately, I can't find the full score on IMSLP.
On the next page, he says
He then gives an inline example with a single pair of notes to show what a staff with two clefs at the same time looks like. I have never seen anything like this before, and did not even know it was possible. Unfortunately, he does not mention any particular work where this is done.
Edit: I just happened to stumble across an example of dual clefs for horns, in Schubert's Great Symphony No. 9, which you can see here, at 12:08, on the 5th staff down from the top. Note that this piece only has two horns, and they are apparently natural (unvalved) horns, so they only get the notes of the harmonic series. Also note that the note in the bass clef uses the older "octave lower" system that Bob mentions. In fact, I believe this note is the horn's fundamental pitch.
Okay, I just pulled out a few scores from my bookcase (looked at some Berlioz, Bartok, Stravinsky and Brahms so far…). In the scores at least, nearly all of the horns are written on two treble (G) clef staves. The scores are all transposing, so I can't see any reason why this wouldn't also be the case for the parts. I do know that horn parts are commonly written with all four parts on two staves in the parts, which is unlike most instruments.
Only the Stravinsky had any bass clef, and this was for really low notes. If you think about it, the strong range of the horn is likely to be fine notated in the treble clef for the majority of the time. The best thing to do is use your common sense; just as when writing for any other instrument that is "borderline" between treble and bass clef (eg. sounding pitch Tenor Sax), use whichever clef is best for any particular passage.
Just a couple of other "interesting" peculiarities about horn parts (sure you might know these already, but hey…) In many scores horn parts have no key signature; they simply have all the accidentals written in. According to my copy of Instrumentation and Orchestration by Alfred Blatter, "When writing horn parts in the bass clef one treats the bass clef in the same manner as is done for piano. (There is an old notation for bass clef notes often found in parts written for historical natural horns; it is written an octave lower than the notation dictated by modern practice and should never be used by a contemporary writer for the horn.) Horn players do not read high notes notated in the bass clef well. Therefore, one should never write notes above G" at the top of the bass clef.
You obviously already know about how to split horns 1-3 and 2-4...
Horns have a very extensive range (From F#2 to C6) so it will depend more on the part itself. If the part is written in the higher range of the horn then a treble clef will be used. If the part is written in the lower range of the horn then a bass clef is used. Typically horns 2 and 4 will play the lower part and if it fits better in bass clef then it should be written in bass clef.
Orchestral scores (as noted already) are usually 1-2 / 3-4, both in G (treble) clef, sounding a P5 lower than notated. Bass clef is not common, but neither is it rare. One thing to be careful of: there was an old custom of bass clef horn sounding a P4 higher than notated. Given that the whole idea of going to bass clef is to avoid excessive ledger lines below the staff, that notation is crazy. Most (not all) modern scores are sounding a P5 lower. It's a good idea to put a footnote on the part about the transposition if you use bass clef. Otherwise, you can get surprises.
Incidentally, in wind band scoring 1 and 2 are the high parts and 3 and 4 the low parts. The orchestral split as odds high and evens low came about in the days when crooked natural horns were in use. A second pair of horns came in to cover the more complex harmonies. Think about it: a Bb horn sounds Bb, F, Bb, D, F, Ab (better to stay away from), Bb, C, D, Eb (better to stay away from again) and F. Some can go above the 11th partial, but not many. So, Schubert wants to go from Bb major to g minor. The tonic triad is G/Bb/D and the dominant is D/f or F#/A/C. The Bb horn has no root in the new key, but can get the 3rd and 5th. The dominant 7 is available (once, pretty high), the root of V is available, but no 3rd or 5th. A D horn would help (a lot), so would an F. Hey, let's add another pair of horns (instead of recrooking in the middle of a movement). Musicians are cheap... And so the first horn is the top of the first pair, the third horn the top of the second pair.
Windbands didn't really get going until after the valved horn in F (or Eb or Bb) was pretty universal, so they never got the habit.
I'll add to the already good answers here that there are some examples of horn parts in the score being re-arranged to (sometimes) facilitate clef changes. Looking at the score for Mahler's Fifth Symphony, the first movement calls for 6 horns, and the parts are arranged differently in the score on a per-system basis. It begins with the parts grouped on two staves with the odd-numbered parts (1,3,5) in one stave and the even-numbered parts (2,4,6) in the other. Later in the movement, there are various permutations:
Some of these groupings appear to be putting similar parts together on the same stave. Others do seem to be workarounds to get parts that are in bass (F) clef all in the same stave, while the parts that don't require being written in bass clef can be kept in the treble (G) clef in their own stave.