If your horse has been allowed to grow their winter coat and are in good body condition they don't need a blanket. Horses prefer to be outside even when it's cold and will do well if they have some kind of windbreak and access to a shelter.
If the horse is not in good body condition is old, skinny or ill they may need a blanket. Older, skinny and ill horses have a harder time maintaining their internal temperature without a shelter or windbreak. Horses that have been body clipped will need to be blanketed.
If a horse has been moved from a warmer climate to a colder climate they may also need to be blanketed until they can grow a heavier winter coat. Horses that have no access to shelter or windbreaks will need a waterproof (not water-resistant) blanket to protect them from the rain.
Horses have the ability to fluff up their hair which creates a warm layer of air around them and acts like a thermal blanket. When you blanket a horse it flattens down their hair reduces their insulating effect and makes them much colder. The same thing will happen to a horse when their coat gets wet or muddy as it flattens down the hair.
When a horse gets wet and starts to shiver they will need extra feed to bring up their body temperature. Never put a blanket on a wet horse as this will trap in the moisture instead move them indoors if possible and out of the wind and give them extra hay.
The way a horse stays warm is by digesting good quality hay which helps them produce heat. If you know it is going to be really cold at night you would be better off giving them plenty of hay instead of putting a blanket on them.
If you choose to blanket your horse make sure the blanket is clean and watch for rubbing of the chest, withers, and shoulders. You also need to make sure you can take the blanket off if the weather turns warm as you do not want your horse sweating. It is best to avoid having the horse wear a blanket 24/7 as horses need to roll in the dirt to help distribute the natural oils.