The attitude that 4x4's don't need chains has ruined my weekend several times, mostly recently... yesterday. Tried to go to Paradise (Mt. Rainier, WA) Saturday. The road was plowed and chains are required to be carried (but not put on). But the road was closed. The ranger said they closed it because too many "4x4 yahoos" (his words) went spinning off the road due to ice. Driving with chains is like driving on rails in these conditions.
These people also get stuck in deep snow and cause trail traffic jams. After spending an hour in one such jam, I was able to plow past the offender with no problem in my Durango with cable chains, even though I had 1/2 the clearance and 1/2 the rubber of this lifted 4WD truck.
There are a number of options for vehicles with low wheel clearance. The H3 with 33's still has way more clearance than most cars. Z cable chains are one. Although, I had a Dodge Durango with 32's, after 1 season with Z chains, they chewed the heck out of my sidewalls. I now use
Spikes Spiders on my Audi (manual also says can't use chains). These things are great. They are a bit pricey ($400) but are worth every penny if you use them frequently. Chains are a royal pain to put on and take off (and you're bound to get wet, muddy, and numb). With Spikes Spiders you just mount an attachment plate at the start of winter (I just did it Friday, took 10 min.), then putting the spikes on (and removing) is an easy operation on the road that takes a matter of seconds, no reaching behind the wheel. It looks like the SPXXXXL (4 X's)should fit, but verify. I'll be getting them again when I get my H3.
Anyway, don't be another 4x4 in a ditch that everyone laughs at.