If he wants to be able to run, he should probably be able to saw the horns off (or rather let a professional do it) on a regular basis.
(Also, his neck would probably adapt somewhat to the strain if he keeps training properly.)
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As for her horns, first I thought they were just odd stumps, but once she started swimming I figured them for some kind of barnacles, but then they remained extended even after she got up and now I'm stumped instead.