I've put about 250 miles on my Alfine, in temps ranging from -10F to 40F. It doesn't shift as nicely as my old derailleur/friction shifter combo, and it slips from time to time in the 5th gear. The only time I've had trouble with the shifting was after the temp went from to 10F to 40F overnight, after which I had trouble shifting down from 5th and 6th gear, which went away after I lubed the cable housings (generally the first thing I do when I encounter shifting problems).
I've been meaning to give the internals an oil bath, in the hopes that it'll clearing up the skipping in 5th issue and the shocking amount of drag in the hub when the I ride it below 10F, but I haven't found the time to do it (stupid homework
). I'd start with running lube through your cable housing, to flush out any moisture that might have collected and could be freezing your cable.