For summer mountaineering in the mild ranges like Sierras or Colorado Rockies, a light-mid-weight hooded jacket should be fine, something like a Patagonia Micro-Puff hooded Jacket or Wild Things EP Jacket. Neither of these work real well over a hood, however, so there is some argument regarding whether to use a hooded jacket in the summer anyways. However, after having been caught out overnight, I find that a hood is real nice, and stows under a helmet fine if you still need to wear your helmet.
For higher mountains or the off-seasons, you need to move to a more insulative parka, preferable with a hood that goes over a helmet.
I love the GoLite Belay Parka - it's warmth:weight ratio is really hard to beat; however, it has a small hood in that it does not go over a helmet and there's no inside mesh pockets to stow your climbing gloves while belaying (a nice feature).
I've climbed a lot with an ID Dolomitti, which has a terrific hood and is pretty warm as well.
But my favorite still remains a Patagonia DAS Parka. Everything about this is dialed in, pockets, inside pockets, oversized cut, long hem, hood, two way zip, good insulation, very breathable fabric. Only downside is that it's bulkier than the Dolomitti, so if that is important to you, you are better off considering Primaloft over Polarguard.
I'm on my second DAS in as many years, and my current one has seen about 50 days of winter mountaineering, a few overnight bivies without a sleeping bag and dozens of long, cold, stormy belays. For me, the DAS has been my best insurance for surviving the night without a sleeping bag. It's very light for what it does too - my size M is 25 oz.