You are much more likely to qualify for a scholarship at any of the Ivies if you can play the French horn well enough to considered for an eventual first chair position in their orchestra. The orchestra repertoire for this instrument is much more difficult and and much more important for the ensemble than it is for the band.
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Couldn’t find any Ivies specifically for French Horn, but schools I did find:
Calvin College
Louisiana State
Winthrop University
Ohio State
Ball State
Juilliard (best music school in the country)

But there are many music scholarships: http://www.musicscholarships.us/
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you should probably think about this logically. all of the ivies get tons of great applicants, many of which play instruments. why would they give you a scholarship for playing when they know that they could easily accept someone else who plays and not give them a scholarship? that person would still play in the band if they liked playing french horn enough.

playing an instrument doesn’t make you special.
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ivy league student

I found some info about getting this scholarship online in this scholarship database – education.mypressonline.com
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I found some info about getting this scholarship online in this scholarship database – education.mypressonline.com
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You should check out Duquesne University in Pittsburgh. They have an amazing brass faculty! The two horn professors there are both members of the Pittsburgh Symphony Orchestra.