We don't celebrate Christmas. My wife is Hindu and I'm a Deist. We're raising our kids with Hindu traditions but allowing them to find their own path.
When our kids started school we made a pointed decision to teach them about Hindu traditions and customs to help give them a cultural identity. This is important to children especially when they are surrounded by a more dominant culture.
We started celebrating Diwali with Bhavna's family. The Hindu calendar is based on lunar cycles, so Diwali either occurs in October or November of the year. Each year we make Diwali a big deal in our family. We've got Christmas to compete with so we make Diwali a vey big deal.
Since Diwali is colloquially known as the "festival of lights", we decorate our home with Christmas tree lights and small electronic tea lights -- a substitute for the traditional open flame diyas. We clean out our home and prepare delicious foods.
The kids know that Diwali is the time of year for gift giving and receiving. This is the time for wish list.
Despite all that our kids want to feel included in the events going on in the larger culture around them. So, each year we setup and decorate a Christmas tree. It has no religious significance to the kids. They just like the twinkling lights. Over the years they've collected little decorative trinkets to place on the tree. Each one represents some milestone in our lives. The Thomas the Tank Engine phase, the “I made it in school” stage, the Pokémon phase (okay that one never ended), the cute panda and fairy princess phase, etc.
So guess this isn't so much a Christmas tree as much as it's a “down memory lane” tree.