temps will be around 5 degrees F during the day  and -10 to -15 degrees F at night ( colder with wind chill).  

Will CLP be fine or should somehing else be used?

According to my Mil-Spec Manual it should be good to go. The trick is once it's cold, keep it cold until your done firing for the day. Once inside, break it down and let it get to room temperature, clean and remove moisture and apply a fresh coat of CLP before reassembly. This works for me up here in Alaska.

I've used Mil-Tech with success at CMP matches in January in Pennsylvania.

when shooting in the winter  here in Northern MN i have had good luck with using Rem Oil.  just a very light wipe, make sure there is no extra.  i shoot at -10 F  regularly.  the only problems i have had shooting at those temps were ammo related.  i got some Olympic 62gr grn tip for real cheap.  they would short stroke and cause all kinds of problems FTF, FTE, DF.  as long as you use something light and thin your weapon should work fine.  most of your malfunctions will be ammo related.  cold weather really decreases ammo efficiency.  not letting you rifle warm up until you are all done is good advice.  the only thing i do different is to leave my guns in the cases for a few hours to warm slowly, i don't get condensation build up that way.  then clean as normal.