Ok so I don't have a twin, but when I think back to when I was 13 (takes a while to load memories that far back these days), my main party memories are all about laughing and having fun with friends. I can't specifically remember "what" we did - but I remember being around friends and having a great time.
So my suggestion would be to focus on making sure the right people attend: All the people that you have a great time with. The rest usually falls into place after that.
If you're looking for a "theme", then I'd pick something that you know you, your sister and your friends enjoy/have in common.
It's a shame the horse riding thing won't be possible, I kind of like the idea of that... But is there anything else you guys all enjoy doing?
A type of music? Dancing? Movie?
If there's a movie you guys all like, you could ask everyone to dress up as a character, and you could watch the movie together or have it playing in the background, with popcorn and other movie-related stuff going on.
Or a fancy dress theme could be interesting if you think people will take part in it.
Or how about a pool party? Tricky to organize if you don't have a pool, but they can be very fun!
The options are endless, I think it really comes down to what you guys all enjoy doing.
