Bow and Arrow is considered connected to music because the verse (2 Sam. 1:18) uses it in reference to a "lament of the bow" (NIV), not in a military reference.
The trumpets are considered used as alarms or alerts, rather than for musical purposes. I suspect the real reason is so that Trumpet Blast and Seventh Trumpet don't get used by musicians out of Musician's Chambers. I've lost this argument in the past, so I don't expect it to change. (But, as I'm working on a musicians deck, I would love to see it happen!)