At those temps, you would be wearing mittens. So the first decision is: can you take off a mitten to open a folder. And you will have to get into a pocket to get to it. You need to be the judge of this. I'll recommend 2 knives. One is a folder that will require that you take you take one mitten off but can still be opened easily with glove on. The other is a fixed blade that can be access with mittens on and the sheath lashed to you clothing, backpack, etc.
For a folder I recommend the Columbia River (CRKT) M21 (tanto or spear point), 4" combo blade. It has a "flipper" that makes it easy to open with gloves on, partly serrated for cutting rope, and it's large so it's easy to handle with gloves on. It does have a metal handle (aircraft aluminum), however, but it is bead blasted and anodized so I doubt if bare skin will stick to it at low temps. If this it problem, there is aother model (M16) with a Zytel handle (a sort of plastic) but the blade steel is not as good as the M21 so will dull more quickly. This is probably not a big deal. Just remember to bring you sharpening equipment (course and fine stones and lightweight serration rod sharpener) and know how to use it. Also, I think the M21 only comes in a tanto point. Get the M21 if you can. Both knives use a liner lock that is the weakest locking system to have on a folding knife. But these knives come with the LAWKS locking system (only found on CRKT knives) that prevents the liner lock from moving and essentially makes the knife very safe and almost like a fixed blade. You don't need any knife accidents where you are going.
The second knife is made my the same company and especially made for outdoors use. It is called the CRKT Hammond A.B.C. (All Bases Covered) Operators in combo drop point. They have a flat point model but don't get that one. It's for rafters so they don't poke a hole in their raft. It comes with a sheath "system" that allows multiple ways of carrying the knife such as lashing it to your chest (upside down for quick access) or backpack. Also has serrations for cutting rope, etc. A great knife that is passed over by many. Made from the same steel as the M21, AUS-8A, a great working, medium quality steel that doesn't take forever to sharpen. Oh yeah, the handle is G-10 and will not stick to bare skin. I've read this model is dicontinued but there are still plenty available.
In conclusion, I would recommend carrying both knives and use the one that is appropriate for the situation. They can both be used for a lot more than just cutting rope. The Hammond is great for food preparation because, being a fixed blade, it is very easy to clean. Don't forget to attach a lanyard to all knives and to your parka or backpack. You don't want to loose them or drop one, point first, on your belayer if you are leading the pitch. (I climbed for many years so know the terms).
Others will recommend knives from Spyderco, Benchmade, and other fine companies. Many knives will do the job for you. But I chose these because of ease of opening with gloves on (the M21), the LAWKS locking system on the folder, and the specific outdoors design and carrying features of the Hammond. What ever you decide on, make sure the blade is partly serrated for cutting rope and webbing easily. At least take a look at these knives before deciding. They would serve you well.
http://www.knifeworks.com/index.asp?PageAction=VIEWPROD&ProdID=4765
http://www.knifeworks.com/index.asp?PageAction=VIEWPROD&ProdID=3909
http://www.knifeworks.com/index.asp?PageAction=VIEWPROD&ProdID=3130
I'm not recommending you buy your knives from this site (although the prices aren't bad). I just like the pictures and text.
Regards and good climbing,
Gary