a remote starter system probably wont have much to do with your starting problems.
the remote starter does the same thing as if the key was in the ignition, it just bypasses the key. i've had a few incidences where the cold weather would screw with my starter. i checked grounds, connections, batteries, and etc with no resolve. it just might be something internal when it gets that cold.. don't sweat it for now..
you can always use RAMMING SPEED to start it up!!!!