Adding a 2nd battery

While dry camping in chilly weather it became apparent that I needed a second battery. I purchased an identical battery to the existing. I'll be routing large diameter cables to connect the 2 together via the posts. These units have both automotive posts and studs. All of the trailers connections are on the studs. My question is, should I split the trailer's connectors between the two batteries or keep them all connected to one battery?

Thanks