I have been a big fan of alcohol stoves for nearly a decade, but I have had trouble with them in cold temperatures (<15f). They are tough to light in those conditions and take forever to boil water or melt snow. Preheating the stove and fuel may help. That said I've carried one for the past four years at the AHU (never used it, but I should have).
This year I'll be using a Whisperlite Int'l because I expect to be melting snow on the second half of the course (I'm skiing again). But since you'll be biking you may be able to get enough water at checkpoints and not worry too much about the stove. If I were biking again I'd probably use an Esbit, though I haven't tried one in the cold yet. As I recall they are as slow or slower than the alcohol to boil, but in a pinch they'll do.