Yes, yes, they do.
The ranges are fine... you could have transposed it about a fifth either way and it'd still be playable at your dynamic.
You had the right idea at the beginning, horn 1 and 3 high, 2 and 4 low, 1 on top, 4 on bottom, right on. But I'm not sure how to handle the crossing between horns 1 and 3, we'll see what Qc says. I would have probably voiced the chords differently so that horn 1 was on top more of the time, being careful because horn 3 draws too much attention to itself being above the main melodic line in horn 1. My solution would be to put the triplet line in 3rd horn starting on measure 1, beat 3, and keep the parts switched just like that from there on, so that horn 1 then has the sustaining tones on top.
Of course,
then again... maybe this applies here? Qc: "The idea is to trick the ear into hearing a single soprano line, while STILL creating interesting inner lines, yet avoiding giving that single soprano line to one instrument."