Yes, turning out horses on newly limed fields may be harmful to them. The initial problem is that they will inhale lime dust while grazing. Even if you use the pelletized limestone there will still be dust from the pellets being beaten up some as they pass through the spreader ( broadcast spreader being worst for this than a drop spreader, of course.).
Next risk is ingestion while grazing. This is why you should not apply any potentially harmful dry product on damp pastures, as some will adhere to grass blades and be chomped up along with the grass.
If you apply to a nice dry pasture, you should wait for 2 to 3 days at least for any dust to settle and for the pellets or dust to settle onto the soil below the grazing line of the grass. Or, ideally, wait until it rains,
I apply lime, and I am of the rain school. Sometimes it happens right away, and sometimes it might take a much longer time, so I try to hold off applying the lime until rain is pretty definitely in the forecast for the next day.
Like anything related to horses, though, if you ask two horse people the same question you will probably hear at least three different strong opinions. One will be, "I do it all the time, and my horses have never had problems. 