Do western people ever decorate their house when they get married?

I have not heard of that in America. But there often appear cars (in movies and pictures) that have been decorated with "just married" images and with cans tied to the bumpers. Is that even a common thing these days?

Usually the reception and events are set up at venues that are not close to our homes. Are the ceremonies maybe closer to home or in homes in India?

Only if the reception itself is held in the home, which the majority are not. In that situation, the decor is generally very subdued because it’s considered a “tight budget” option, even though many backyard weddings cost more than one at a regular venue. The exception is a cake and coffee reception, but even then chairs and tables still must be rented and the backyard big enough for everyone. But any decor will be minimal if any exists at all.

On my father's side of the family, they did this in the wedding colors. The dècor the following morning for the family breakfast.