I assume it's up north or in the mountains and it gets very cold.
Just because the furnace can be kept at 40-45 degrees does not mean your cabin can be, if you don't drain the pipes.
Are your wet walls exterior? Do you have a basement or a craw space (open or closed). We have a place at 9800' that we stay at a couple time in winter (snowmobile only way to get there). I would never leave the water on, even when we know we are going to be back in a couple weeks and leave the heat up. What are you going to do if you have a power failure?
If you don't drain the pipes, make every effort to keep the pumbing warm. Open cabinet doors under sinks, open bathroom doors etc.
Dont forget the waste lines/toilet and antifreeze (RV not the auto antifreeze).
If you can get to your cabin in the winter, I would. Our place is completely different in the winter and snowmobiling is fun.