In around 2000BC the Chinese invented what type of food that was a mixture milk rice and paste with snow?

The food you are describing is Bing Su. It is a Korean shaved ice dessert, not a Chinese invention.

While there is no record of a Chinese food combining milk, rice, paste, and snow from around 2000 BC, it is possible that a similar concept existed. The Chinese have a long history of incorporating shaved ice into their desserts, and milk, rice, and paste are all common ingredients in Chinese cuisine.

However, the specific combination you describe is more closely associated with Bing Su, which originated in Korea and has become a popular dessert worldwide.