Don't know about other countries, but in Russia, mobile operators just love to SMS-spam you with tons of advertising. Even though they provide option to opt-out, but even then will still accidentally send messages. Some carriers even used to spam in USSD queries results, appending ads to useful information (like account balance).

(Therefore I doubt it was New Year congratulations. Probably just an ad (may be New Year-themed, though))

It was most likely an automated "Happy New Years" message from her carrier.

Just use an Android phone and set up Tasker to trigger on a special keyword in the SMS, not just any SMS.