thats great that you got your girl into riding. We need more estrogen on the slopes! I dont know if you live near any snowboard shops, but I highly reccomend taking a trip and trying on some gear to see what she likes/ what fits right. Womens gear is notorious for fitting funny and all of the companies cut their clothes different.
As per my experience I would reccomend looking into
32 lashed boots.
Burton gore-tex glove/mitt. (i've had these for 2 years and m hands are always dry and warm and they come with liners)
Suburban is right the eg5 goggles are great and they even come in spherical now.
Betty rides makes sick girls outerwear, but I usually buy what fits good/has a good waterproof rating and is on sale.
Depending on where your riding,buy a facemask.
As far as a board, everything is on clearance now dogfunk.com has some great deals and their customer service is awesome.
Same with bindings, dont cheap out because cheap bindings break and thats no fun.
Anyways i've got to leave for work, but if i get some time later ill hook you up with some links for female snowboarding gear. For now have her visit, Shred Betties: A Women's Snowboarding Magazine