Rattler Race from Windows Entertainment Pack 2

This was released in 1991 for Windows 3.x.

The following are the rules, copied from Help - How to Play - Overview:

RattlerRace is a game of speed and agility. You are a hungry snake, and you are trying to eat all the apples in your room before going out. Problem is, you grow with every bite, and you have to make sure you don't eat yourself. Sometimes you compete with computer snakes, too, and sometimes you have to beware of bouncing balls that can knock you out.