There's nothing wrong with saying Happy birthday to someone, weather its an ex, friend, family anyone.

But, If it's a previous ex girlfriend you had, and the relationship was rough, thing didn't go well or end off good, then you may be better off just leaving it alone.

There's only 3 things that can happen...

1: you can say happy birthday, and she replies (weather it will be rude or not)

2: you can not say anything, and let it pass by. And.. what else? She can't get mad right... I mean from what you said she was being rude to you, so why would she care if you Didn't say Happy birthday?

3: or you can Say Happy birthday and get No response back. Which basically says (in my eyes) "thanks for saying Happy birthday, but not thankful enough to care, or reply. Period.

I always taught to be the bigger person.

My answer: go for it! Are you happy without her?. If so, then what harm can it do?

=]
good luck!