I think the crux is the move or two up to the traverse. After the initial easy traverse out of the belay it's fairly easy to take the first step up and rightish. After that it took me a while to figure out how I wanted to continue up. The traverse left after moving up is fairly obvious, and you're golden as soon as you hit the big block with the pair of pitons jammed underneath it. The last section of overhanging jug hauling isn't a gimme but it's just a matter of holding on.
I thought the crux was the crack. The rest was on good holds with good rests. The rock around the crack is smooth so you can't just slap a foot anywhere and expect it to stick. There are enough to get to the top of the crack though and there are decent holds there (I think I could wedge a hand/fist near the top, and there was another good hold right and above the crack). You can also go out to check out the crack and retreat back to the alcove to rest.
After the crack the start of the traverse left was tricky - I don't remember the details, but maybe just not as positive holds? There is a pin and I think I did one more move past it to a massive jug. I'd recommend committing to go that far instead of tiring yourself trying to clip the pin early. I don't even recall if the pin is any good. There were a few on the route and I think at least some were junk.
From there you can more or less take a nap around the corner before the juggy, pumpy, awesome finish.
Great climb. As previously stated moving up the crack and getting established in the leftward traverse after that is the crux.
Climb is in a right facing corner and likely to be extremely cold. I've always done Le Teton on hot summer days as it tends to be always cool and in the shade. Maybe not the best choice for a cold day.