FWIW-
I run 37's on my SUT and they rub a little bit.
The extra inch of ground clearance I got over the 35" stockers has helped in a couple of situations while wheelin it. plus it looks cool.
m To run 35's on the H3 would help about the same in comparison.
Now, the tire you are looking into is a great tire for off roading (just my opinion) and has an overall diameter of 34.8" x 12.3" wide. Now if you look on their web site it shows an aproved rim width of 8" to 10." So if it were me, I would not run that tire on the stock rim. ...just my 2 cents.
Also, this tire is great on the rough and loose stuff, but I'm sure it's like my BFG MT's, they suck on snow/ ice. They're not siped (little grooves in the tread blocks).
Even switching to a 285 GY MT/R or BFG MTR will change the appearance on your rig and give you better bite in the mud and rocks.
Good luck,
Tim.