With lots of good insulative layers, you should be fine, particularly in the trailer where the walls will trap body heat. Full body snowsuits are great. REI makes a
down one for infants/young toddlers, that if anything is likely to overheat them in a trailer. My kids are more exposed and we've had very good luck with snow suit + balaclava + gaiter (
http://flickr.com/gp/fletzet/sWb2C6).
Turtle fur makes kids balaclavas for under-helmet wear:
http://www.turtlefur.com/kunder.php