Outdoor sex is important for a marriage. I built a private balcony directly off our master bedroom, it overlooks the pool. Has a sturdy rail.
Just figure out a time to be honest with your wife, a good rule of thumb (this works for employees, kids you are coaching, friends, whomever) is to give her 3 things you are happy with and 1 thing you would like to work on and how you would like to go about it. Another thing, I noticed is that she does the books and shopping, etc, this can be much more stressful than the physical chores you are doing. Trust me, if my wife gave me the choice of doing the dishes and bathing the kids over running the books, I would take the former every time.
My wife really has no interest in the outdoors either, but I have never gave it a second thought. I don't think it is even something that should matter if you are compatible most other ways. You speak of lethargy on her part, watching Oprah, probably some "real housewives of whatever" too. IMO a lot of lethargy found in Americans come from their diet. Highly processed foods cooked in hydrogenated oils just make you tired, they give you enough energy to get through the day and just crash out at the end of it front of the TV.
I think if you could get her to go for it, start by trying to work on prepping and eating whole clean foods together. Preparing meals together, making the shopping list, etc, could be a good start.
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WDFW - Turning outdoorsmen into golfers since 1994.