When riding a horse, in first person, looking forward, you get that weird, interrupted sound that just hurts your ears. You can ride in third person, or just look up or down while riding to fix it — but that can't be the goal.
In certain ways, this also affects normal walking and traveling with a minecart.
Expected:
The overall walking sound produced by the player is not directional to the player himself, and always plays mono.
Observed:
The sound is directional to the player, which causes weird interruptions and even distortion.
I cannot reproduce this. What audio device and settings are you using? Right-click on the volume icon on the taskbar, click on Sound settings, and click on your audio device in the Output section.