“My question - do I keep up the moisture content?”
Depends upon how quickly you want it to decompose. If warmer weather is coming (anything above 40 degrees and a good stir once in a while keeps compost piles breaking down) you can wet it down if you need to.
I have four bins (about 4’ tall, 4’ wide circles of pig wire) which I completely ignore, other than to throw “browns and greens” into them. Every year, we dump over the oldest bin, and use that, then that oldest bin becomes the youngest, etc.
Since they’re under yards of snow right now, they’ll have plenty-o-moisture to start up again when we get steadily back up to the 40’s (April, if we’re lucky.)
So you do not turn your piles every so often?