Not at all - but the vast majority do. So, most of the horses you see will have brown eyes, with some small variation in shade.
In fact, four eye colors are observed in horses:
1. Brown. Brown is the "standard" color for equine eyes and is seen on the vast majority of horses.
A brown eye. Source Waugsberg via Wikimedia Commons.
2. Blue or "wall" eyes. Wall eyes are most often seen when a white marking crosses the eye - in fact, sometimes the eye can be part blue and part brown. They occasionally show up on their own. Wall eyes are a rich blue with an almost crystalline effect to the iris.
3. Dilute blue. Cremello and perlino horses also have blue eyes, but this is a different shade of blue - these eyes are a very light blue almost shading to grey.
The top image shows the pale blue eye associated with cream horses, the bottom one is a "wall" eye. Source: Countercanter and Ejnot via Wikimedia Commons.
4. Amber. Amber eyes are seen only with the champagne gene. The foals are born with nearly white eyes that fade to golden amber or a shade similar to human hazel by maturity.
(I wasn't able to find a good picture of a champagne horse eye - if anyone has one they'd be willing to let me use I'd appreciate it).
There's a superstition amongst some horsemen that blue eyes are associated with blindness or compromised vision. This is not true; nor is there any known association between eye color and hearing in equines.