Turning horses out in the snow can lead to a number of health issues if appropriate measures are not taken to ensure their safety and wellbeing. Some of the potential health issues associated with turning horses out in the snow include:

1. Hypothermia: Horses can suffer from hypothermia if they are left out in the cold for too long without proper shelter or protection. This can lead to a drop in body temperature, which can cause a number of health problems.
2. Frostbite: Horses can also develop frostbite if their extremities are exposed to the cold for too long. This can lead to tissue damage and even the loss of limbs in severe cases.
3. Dehydration: Horses may be less likely to drink water when it is cold outside, which can lead to dehydration. This can cause a number of health problems, including colic and impaction.
4. Slip and falls: Horses can also be at risk of slipping and falling on icy or snowy surfaces, which can lead to injuries such as sprains, strains, or fractures.

To mitigate these risks, it is important to provide horses with adequate shelter, such as a barn or run-in shed, where they can seek refuge from the cold and wind. Additionally, providing horses with access to fresh, unfrozen water, and ensuring that their feed is appropriate for the cold weather can help prevent dehydration and other health issues. Finally, monitoring horses closely when they are outside in the snow can help prevent slip and fall accidents and ensure that any injuries are treated promptly.