Rainscreen for board and batten siding?

I’m re-siding some board and batten siding on my cabin after doing some work and I’m unsure about adding rainscreen and furring strips between the sheathing and the siding?
Boards are 1x10 pine and the battens will be 1x3 pine. I was planning to use 30lb roofing felt or Tyvek between the sheathing and the siding with no furring strips.

There is an attached deck and the siding will cover the wall down to about 4” off the deck so there will be some snow buildup against the siding in winter. It’s a 3 season cabin in NH.
It’s a very small section of the cabin- Approx 10 feet long overall
Should I be using furring strips? Seams to me that furring strips will restrict any moisture that gets behind the battens from draining down.

Am I good with this plan? I’d rather not build up the thickness of the wall too much making it tougher to trim around the door and windows.

Thank you!

 

Here’s a pic showing the old board and batten siding. Thx