Horses are integral to the history and culture of Iceland to the point of having an exclusive breed of horses with their own unique gait yet you can still eat horse here.
Only from a different cultural context, there isn’t an objective idea about what’s correct here. The idea that horses should be privileged because they are historically important is itself interesting. Particularly in terms of how historically they were widely eaten. I also think there is a bit of retconning going on where our views of the animals now are assumed of our ancestors. For example I’m British and horses are generally not eaten but this it’d be ahistorical for me to claim that this was true even in the relatively recent past.
Also the idea that cowboys are uniquely horse based when vast swathes of the world was also using horses ubiquitously at the same time!