I have personally had horses swim a pretty swift river just to... I have no idea why. They had about 2500 acres behind them and a house, shop, and tractor storage that they went to. Go figure.
Based on that, I would fence the lake on the pasture side and make only a small area that allows access for watering. Also, with the shape of horses hooves they tend to beat down the flora around watering areas, increasing the risk of erosion. More important along streams, but still, you probably want to protect what grows around your lake.
If you find that the horses are damaging the area that they can access, gravel can be put down.