I played Moscow Country Club in 2008. It’s OK, parkland running through a pine forest, definitely a lot of trees but I don’t recall it being terribly claustrophobic. It’s part of a resort complex outside of the city (at the time it was a Le Meridien, but it looks like that branding is gone now). It wouldn’t have looked out of place in the north woods of Minnesota.
The golf wasn’t all that memorable (other than the novelty of playing what was at the time, I believe, the only 18 hole course in the entire country). What I remember most was that after the round, in the middle of the afternoon, the one woman working in the pro shop had just left and locked up, so we had to hunt someone down to open up so I could buy a shirt. Also, the guys working in the bar didn’t want to sell me a Pepsi at the turn because they would have to give me change for my 500 ruble note, which was about the equivalent of a $20 bill. (That was a theme the entire week, Russians hated giving change. My hosts took me to a McDonalds on the way back from the course and the cashier haggled a deal with our driver/translator, she basically gave us a discount so she didn’t have to break a bill.) Lots of interesting memories from that trip. It was the week Medvedev was “taking over” for his interregnum term so we got to see dress rehearsals for the big military parade through Red Square.