I'd argue the modern equivalent would be anything you can mount/move with a pick up or a trailer. So a machine-gun, but not a howitzer.

Either way, those "field pieces" were the property of the state, that it was expected to supply by the AoC treaty, rather than something individuals were expected to bring along.

The Constitution explicitly states the government may grant "Letters of Marque and Reprisal" to private citizens.

What are those private citizens attacking enemy ships with exactly - strong words?