Horses, unlike cattle, are hindgut fermenters.  The majority of their microbial fermentation occurs in the large intestine, after food has already passed through the highly acidic simple stomach.  The advantage of this type of digestion is that the horse gets first dibs on easily digestible nutrients before the microbes get to them.   Conversely, disadvantages are that horses are less efficient at extracting nutrients from poorer quality feed because there is no rumination (re-chewing of cud).  Accordingly, horses typically eat more than cows do, chew more thoroughly before swallowing, and graze for longer periods of time throughout the day and night.

With regard to nutrient requirements, horses, like all animals, require the six basic nutrients: Water, Carbohydrates, Protein, Fat, Vitamins, and Minerals.  

The National Research Council has a really neat online database that you can use to figure out your horse's nutritional needs.  Click here to access instructions to the NRC database.  
 
It is also important to note that Water is essential to keep the animal hydrated and prevent an intestinal impaction or colic.  Horses typically require one-half gallon per pound of feed fed (or 10-12 gallons per day).  More water may be required for work animals, animals in extreme temperatures, or animals fed very poor quality or dry feed.  Also, make sure the water is not freezing cold because the horse will drink less if it is too cold. 

The University of Minnesota also has a good article on feeding horses in the winter.  You can read it by clicking here. 

In short, "For every degree below 18°F the horse requires an additional 1% energy in their diet. Many people believe that feeding more concentrates (because they are energy dense), will help keep the horse warmer. However, there isn't as much heat produced as a byproduct of digestion, absorption and utilization of grains as there is from the microbial fermentation of forages. Thus, increasing the amount of forage in the diet will help meet the increasing energy needs and will result in an increase in microbial fermentation which will help keep the horse warm. For example, if a 1000 lb horse needed 16 lbs of good-quality hay each day when the temperature was 18° F, its requirement could be expected to increase by approximately 2 - 2.5 lbs to 18 -18.5 lbs if the temperature dropped to 0° F. The increased dietary energy requirement would be even greater if the horse didn't have access to shelter."

Quick Reference Guides

Nutrient Requirements for Horses
Caring for your horse in the winter
Nutrient Needs of Horses
Basics of Feeding Horses