We are currently commuting via trail-a-bike, and I highly recommend it! Kiddos get their blood pumping before school, and they start the day with their brains "on"...not to mention, already exercised means less likely to act hyper in school :)
As for keeping warm in the trailer, layers, layers, layers. Also, you might consider a layer of insulating foam under the seat and perhaps even across the back to give more R value. Sure it might get muddy or dirty, but keeping the kids happy and comfortable about this arrangement is really the key to success for long term biking plans.