Bb is the natural scale starter for brass combos, so Bb minor is a natural for funeral marches. Brass instruments are decidedly not equally tempered, so different minors have different characters.
If you are playing a natural trumpet (valveless), and that's sort of the instrument type that was quite a bit around when the key associations were established, then a minor third is sort of an awkward interval to play. The interval is supposed to be 6:5, but in the overtone series you instead have to revert to something like 19:16 which is 18 cents flat.
So that gives you a somewhat exaggeratingly depressed minor scale when played with valveless trumpets. While the valves on modern instruments offer more possibilities for getting the intonation closer to equal temperament, all of the possibilities still are tinged, with the instrument better-suited to the Bb major scale.
So even nowadays, not every scale is equal. But the "ideology" around various scales developed way before modern instruments, with the scales (both major and minor) starting flat from C being mostly natural to brass and some other wind instruments, and the sharper keys being served better by string instruments (also remember that in Renaissance and before, even many bowed string instruments had frets and thus were somewhat fixed in the scales the tuning got optimized for).
A modern piano, and to some degree modern orchestras are not really making different scales sound all that much different in character. But the traditional associations are not completely arbitrary but founded in the instrumentation available and its characteristics in different keys.