No Gage, neither parent has to have blue eyes to throw a blue eyed foal. It can skip generations. CockRobin has blue eyes & he sired Nickelodeon, who only had a star, snip & white coronet & brown eyes. Nickelodeon has gone on to sire many blue eyed foals from brown eyed mares.
Here are a few of mine....
Kickapoo's A MayZing Moon
Kickapoo's Devine Miss M
Moonie has two crystal blue eyes & Lacy has one blue/one brown.
Double Dilutes- Perlino and Cremello, always have blue eyes. In Pinto, H/Z for Tobiano would not have blue eyes as Tobiano does not cause blue eyes, same for Sabino- the confusion happens when a horse H/Z for Tobiano carries another gene - Splash or Frame, that causes blue eyes. Only Splash can be H/Z of the two blue eyed causers- as Frame is lethal in H/Z form. I would think it would be a given that Splash in H/Z would have blue eyes- I am not sure that it always has them though- there could be exceptions, there usually are, as soon as a rule is made