For winter conditions or long term storage in the pack, hard to beat lithium batteries. I cant recommend rechargeable batteries unless you have a backup. Doug Paul has done extensive research on batteries and rechargeable in the past and maybe he will weigh in.
You called?
Lithium primary (non-rechargable) cells have the lowest temp limits (nominally ~-40F) and the best shelf life (~10yrs). NiMH and LIon (lithium ion, rechargable) are next best (~-20F), alkalines next (~0F), and leave your carbon-zinc (dry) cells at home. (These temps are approximate--in practice the actual temp limits vary according to the details.) Lithium primary cells are also lighter than the other types of cells.
FWIW, I carry 2 or 3 headlamps and spare batteries (particularly when doing through-the-night ski trips...
). I have dropped batteries in the snow while changing them, it can be hard to change batteries with cold fingers, and lights can fail. And, as jniehof noted, a new battery can be defective or discharged. A second light can also be helpful when changing the batteries in the primary light. For day trips, I generally carry fully-charged NiMH cells. My spares are NiMH or lithium primary.
I only carry lights with field exchangeable batteries.
Lights can get turned on (and the batteries drained) in the pack. If a light does not have a secure switch, reversing half (1 is sufficient in a 3-cell LED light) the cells can ensure the batteries will not be drained even if the switch is turned on.
LED lights are generally more efficient, more tolerant of weak batteries, and more reliable than incandescent lights. I switched to LED years ago and haven't looked back.
Water-resistance can also be helpful if you need to use the light in the rain, may get condensation in it (eg putting a cold light in a warm, humid pocket), or drop it in the snow or water.
Doug