1 and 2 will probably do just fine. I was in Norway in Feb this year shooting the Northern Lights. From memory, most of the stuff was done using an 18-55WR lens on a K10 or using a Pentax fisheye on the K10. I took the Sigma 17-70 but it was a pile of rubbish and really DIDN'T like the cold at all and kept stopping working. I can't remember using anything much longer than this. A good (carbon fibre) tripod and cable release are also needed. Also, remember, no filters on the front of your lenses either as this causes problems. There's a guy in the USA somewhere who has a blog about shooting things like the "lights" who produced an excellent list of do's/dont's along with some excellent images.
How to photograph the northern lights with a digital camera.
Most of the time I used manual focus anyway. One other thing I found useful - a 90 degree finder!
Where are you planning to go? I've been to Iceland twice, but never in the "cold".
Lenses misting up is also a problem you need to be aware of. Make sure you pack lots and lots of "good" thermals and make sure you test your stuff before you go out there...you might get a surprise about what does/doesn't work as well as you think it might. Other useful tips - a red LED head torch, mittens (not gloves), inner gloves as well as outers. Your feet will get REALLY cold if you are stood around for a long time as well - I used heated insoles for some of the stuff I did.