Pete,
Don't know if I'd recommend the turf tires if you get a RTV. The HDWS are a little more aggressive but not enough to tackle mud beyond a couple inches.
Many of us have bought a set of aftermarket tires (and some of us got rims as well). I got the rims as well thinking I would have a summer set (OEM HDWS tires/rims) and a winter set (aftermarket tires/rims). I got the Maxxis Bighorns and they seem to be one of the favorites for mixed terrain (everything from grass, mud, loose gravel, pavement...). So far, I won't be changing back to the OEM as the Bighorns are great regardless of the terrain. I've attached a pic so you can get an idea of the tread.
There are more aggressive tires out there (I.e. 589's) that look/act similar to R-1's. They'll take you through anything but may leave marks in the process. Look at the tires in the next post. These are 589's.
As for getting stuck, unless Mrs. Wingnut is driving in areas you look twice at with your CUT, she should be fine. My RTV with the Maxxis tires and no lift kit gives me around 9-10" of ground clearance on the belly. I've had it in soup/mud that was probably 2-3' deep (although the base was flat so I didn't drag the belly and I won't do that again due to how long it takes to get the mud out of everything).
For driving in the yard this time of year, the marks I'm leaving in the yard are pretty much just the tread pattern. Nothing you would twist an ankle on and they'll come out with a lawn roller.
As for weight, I don't know what your golf cart weighs. The RTV with a passenger is right around 2000#.
I don't think there will be any issue with chains if you use OEM tires. Some of the aftermarkets are a bit taller which may cause an issue with the fenders. But if you go aftermarket, you won't need chains.
It sounds like now is the perfect time to get the dealer to bring you a demo unit. I would probably have one with the ATV tires because they're closest to the tire you would need.
Brian