I think "band" somewhat fits, but only because it is a blanket term that can include any sort of band--marching band, concert band, wind band, etc.
Same thing for marching band.
I'd have to do a little research to figure out if we have a more specfic term for this sort of marching band make-up ...
Hmm, I've just found websites from Spielmannszügen that do not fit the description I posted in #1. They seem to include other instruments--this one
, for example, or this one
(which only consists of brass instruments and therefore fits the description "brass band").
I guess if there is not a consistent instrumentation for the German Spielmannszüge, the best English translation would indeed be "marching band" and "band", since those include any instrumentations.