I climbed a 14er when I was visiting Colorado... was going to do two more but weather kept me away. Since I did it during daytime hours I did not need a headlamp but I kept the Petzl E+Lite with me to use around camp (I packed my way up to the midpoint and summited the next day). It is a very good, very lightweight headlamp but a bit underpowered. It takes two lithium coin cells so it's always ready to use when I really need it.
Anyways, I think the Zebralight is going to get a lot of recommendations here. They are a little bit on the expensive side but some of the headlamps being talked about over at 14ers.com seem to be bumping up against that price range anyways.
What we like about the Zebralights is that they are extremely small and light, durable, and take just one battery -- an AA, a CR123 lithium, or an 18650 lithium-ion rechargeable depending on the model. They have what we call a floody beam -- which is a light output that is spread wide and evenly, which allows good close-to-medium range vision but not so good for long range (10m+). This should be fine for the large majority of users.
For those interested in ordering a Zebralight, I strongly recommend 4sevens.com (Disclaimer: David is a good friend of mine and I do work for him occasionally on the side.) Use the "CPF8" coupon code for an 8% discount. Free shipping.
Absolutely it's a good idea to use lithium or lithium-ion batteries as they perform far better than alkalines in cold weather. If you cannot afford to use a lithium or lithium-ion based solution, NiMH rechargable work better than alkalines and are readily available.
Being a bit of a flashlight nut the headlamp I will take with me when I go backpacking next year will be the Surefire Saint. The smaller, lighter one, the Surefire Saint Minimus is available now, with the full-size Saint coming later this year. It is around $140 and made in the USA. If you have military connections you can get the Saint for around 20% cheaper than MSRP.
Please feel free to quote me over on your forum, but I ask you attribute the post to me (link back appreciated).