Unfortunately that tactic will only work when the noise is the only sound present, (in your example no voice present, i.e. the gaps between words), then you can use a gate to squelch the noise down.
Free noise gate plug-in for Audacity here … Noise Reduction, a Judgement Call - #6 by Trebor
If the horn is one frequency (and a few harmonics) it may be possible to reduce/remove it with a notch filter … FM Stereo "noise" and its removal - #2 by Trebor