My friend aksed me if I would go snowboarding with him. Thrilled I agreed. A couple days later I found out that my best friends ex boyfriend is also coming. I told my best friend that her ex is coming. She didn't say anything about it so I thought she's OK with it.
I still had a weird feeling about it so I asked another friend if she would come, so that I could be with her and so I could ignore her ex.
Well I found out that my best friend is really mad, that I went snowboarding with her ex. I tried to call her, she won't pick up. I wrote her an email she's not writing back.
What should I do that we can talk about it?

YourI'm a little confused. Are there multiple "best friends" here? You were invited snowboarding by your best friend, and you best friends ex was invited also? Did the friend that is mad invite him? Just confused by the wording.

How long was it after the breakup? Days / weeks? Why was the Ex invited in the first place?

--Friendship Rules are touchy. Hanging out with an friends EX is always going to start trouble and make people upset. Why

It's an immature teenage rule that best friends aren't allowed to even so much as say to an ex, regardless of who broke up with whom, but especially if the best friend was the one dumped.
You did what you could.
Send her an old fashioned LETTER saying what happened. Mail it. It has more meaning.

Find a way to explain to her what happened and see how she responds. You can't control how she feels, but you can do your part in showing her that you didn't mean to hurt her.

Either write a letter or email. It's better to have it written out because when it's on paper, she will see it more clearly.

I'd say that you just have to say sorry and if that didn't work then you did what you can and the rest is up to her