Hiking above 10,000 feet you won't have alot of available firewood, or much of anything to string a hammock between (unless you find some really conveniently placed rocks). I vote for a bivvy for shelter, although I tend to carry a lightweight tarptent on longer day hikes where I could find myself out at night. The tarptent isn't a 4-season tent, but I know from experience it would keep me moderately warm and dry, even in snow. I also recently became an owner of a Stephenson 3R, which is a 4-season tent and takes no more room than the tarptent, so I may switch to carrying that on longer hikes. Around here nighttime temperatures and weather call for insulation and staying dry, so carry what you need for that - at minimum a 2x2 sitpad (always useful), better yet a z-rest or better still an inflatable sleeping pad. But at 10,000 feet I think you will want your insulation enclosed in a bivvy or tent to keep it dry and you more comfortable. And imho if you don't already carry enough clothing to stay warm and dry through to the end of every hike, you shouldn't be going out at all.

I spent a night in my backyard in one of the AMK solo bivvies a few years back and wrote about the epxerience here. I was fully clothed as though I was on the trail and spent the night comfortably beneath a friendly cedar in my yard, no real condensation although I've heard others say I must have been drenched with it (I wasn't). Comfortable, but not alot of insulation value. I carry an AMK bivvy in my pack at all times - for the same reason that I once carried a Tacoma Mountain Rescue orange plastic emergency tent, as a last ditch shelter - but usually that's my giveaway to a fellow hiker who needs shelter / assistance (if you can't move them, you can always cut a $11 bivvy open and lay it over them for shelter).

And don't forget a bit of food - food before you settle down for a long cold night food will start your engine (metabolism) a bit and warm you.

I recently read a trip report from a wahoo who went out bushwacking over tough terrain and spent an unexpected night on a steep traverse, no shelter, no clothing except his shorts and a fleece top - and borrowed food and water from his fellow hiker, who followed this twit up the mountain. Lots could go wrong in that scenario, but it didn't, so actually he didn't really learn very much from it. The gods smiled on them so it didn't rain on them all night. Coulda though.