Hello Elk! Actually, I own a 2001 H1 and a 2005 H2, I also own a 2002 Jeep Sahara, and right now I´m considering in buying an H3 for my wife.
you may want to see my gallery, there you will see some nice pictures of what off road means.
I drive my H1 for extreme off roading and long trips, my jeep Sahara for really extreme off roading but short trips, and my H2 SUT just to drive it in my hometown, ahh, I also usually use my H2 SUT to pull my jeep when I participate in 4x4 challenges
I have tried to use the H2 in off roading thing but is too weak for that.
Me and my friends are members of a 4x4 club and we use to go off roading every weekend, sometimes we use to go on long trips to the beach, the mountain, desert, etc
Two months ago we suffered a terrible flood here, and emergency services asked for our help to rescue some people, we used our 4x4 equipment.
As you see, I really know what off roading means!! and also I know that the H2 is not recommended for off roading, maybe it´s useful to drive it in secondary roads!