I've been wheeling the local trails a few times with other Hummer owners, a mix of H3s and H2s, plus a couple non-Hummers. For the H3s, 33" tires seem to be the standard and some of these guys hit Moab regularly. I'd put sliders and UCP at more important than going up to 35s. I will say with the longer wheelbase in my T and before I leveled the front (raised from 19" to 23") I scraped over a couple things that H3's on 33s didn't. My next set of tires will be 35s. My T is my DD, but I work from home so no long daily commute. If I had a long commute or was still driving an H3 I'd probably stick with 33s - plenty capable of real wheeling.
Since the conversation is turning toward which tire.. I'll be be going with Duratracs, BFG ATs, or General Grabber AT2s. Probably the Duratracs but not 100%. I ran BFG MTs here in UT when I was driving a jeep and they suck in light or hard packed snow. My personal requirement is the snowflake on the tire which unfortunately limits my options.