Dogs are a big thing for a lot of horses. I went riding in a field once with a friend and her dog. My boy was still young so when I asked for a canter he did what most babies do and bucked, I lost my seat and he ran off. But then my friends shepherd took off after him and chased him all over the place.... it wasn't a good experience. Do you have any friends with dogs? If so, ask them if they could help you with sacking out your horse. Hold your horse in the middle of a ring (in a rope halter so it has no chance of breaking, we want all animals to be safe) and have your friend make the dog bark (a good dog can be taught to speak easy) have her make the dog bark over and over until your horse doesn't care. Or you can use a different approach and say "Noise" when the dog starts barking, it will warn your mare that their might be a loud noise soon but she doesn't need to be fearful cause you know it's going to happen and as the lead horse, you aren't afraid and neither should she.
Now get your friend to leave the arena and *hide* and have your friend get the dog barking again at unexpected times. Have her make the dog be very quite for a long time and then start again, make it so your mare doesn't expect it. When you feel comfortable start doing simple groundwork while the dog keeps barking unexpectedly. Now make your horse stand again and have your friend bring the dog out and start bounding around and playing with it, get it to move in unexpected ways so your mare learns a dog can be goofy and move in a crazy manner, but she's ok, because you are not afraid.
Now one of the fun parts, make sure you have good control over your mare and have your friend walk the dog up on a leash, then them interact and say hello, then have your friend walk away, do it till the horse no longer is spooky about this.
Now have your friend stand near you, in front of the horse and call their dog from a sit-stay. The do should be trained well enough to run right up to your friend and not to the horse, do this till she's not worried, then slowly have your friend move closer to you and your horses head, having the dog run up to her. Your horse will learn that a dog can run up on her but it's ok cause the dog won't hurt her.
The next step would be riding your horse and having your friend playing with the dog nearby and making it bark and run up in front of your mare all over again. Your horse will slowly gain the confidence it needs to understand that yes, this is a predator, yes it could be dangerous, but she's not allowed to run away or misbehave as long as you are with her cause you are going to take care of her. Hope that helps! That's what I did to get my horse used to dogs again.
Everything takes time, do not rush her or you will end up in danger. A good horse has had time put into it so it understands not to panic every time something unexpected takes place. Always end her lesson on a good note when working with something she is uncomfortable with, do not use punishment for her behaving like a horse and never end her on a bad note. She'll get it and you and her will be safer because of it.