What's interesting is that many New Year traditions share the same underlying idea: clean out the old to make room for the new. In Thailand they celebrate Songkran, where people throw buckets of water at each other as a form of purification and renewal, so it's similar to the Greek ritual you mentioned earlier. Scotland definitely does "first-footing," but there's more: in Brazil people dress in white and go to the beach to make offerings to the sea, asking for blessings for the year ahead.
In Denmark they have something pretty brutal: on the night of December 31st, people smash plates against their friends' doors (with permission, of course!), and the more plates that get smashed at your door, the more friends you have and the luckier you'll be. In the Philippines they toss coins in the air during the New Year countdown because it's supposedly supposed to attract money and prosperity. Some countries like Scotland also have the custom of opening doors and windows right when the year changes so that the bad stuff leaves.
What I'm seeing is that even though you eat grapes and wear colored clothing (which also have that touch of renewal), almost everywhere people want to do something physical: break something, throw water, toss coins. It's like we need a tangible gesture to convince ourselves that we're really leaving the old behind.