The first thing that pops into my head is that you probably stayed astride of her and sitting like you would normally ride on dry ground. Generally speaking, horses are good swimmers, but they can only carry so much and keep their head above water. Think of it like this, a horse trying to swim that is carrying a rider in normal riding position is about like a person trying to swim with a big brick in their arms above their head. Because of the laws of buoyancy, more weight above the water automatically makes their body go down farther in the water...and if they aren't fit enough to compensate for the added weight pushing down on them, then they will not be able to keep their head above water.
That's the reason behind all the cowboys in movies are always seen either getting off to the side or hanging onto the cantle of the saddle and floating for themselves, only using the horse for forward momentum.
The biggest problem with that is it can be exceptionally dangerous, especially for someone who isn't terribly experienced with doing it properly. It would be very easy to get one of your own legs kicked and end up with a broken bone or.....she could panic and start looking to you to keep her safe and end up drowning you by swimming/pawing over the top of you.