Sometimes you can find urine spots that appear red in color and become concerned that it may be blood. In 99% of the cases the red color is not due to blood, but due to the oxidation of some of the compounds in urine. We see it more in the winter because it stains the snow.
A horse with blood in its urine may show abnormal urinary behavior (including colic, an inconsistent stream, or stopping and starting) or abnormal drinking behavior (increased or decreased drinking). Blood clots may also be seen, and the red color would also occur in the shavings. If your horse is acting normal then do not worry about the red color, if anything changes I recommend talking with your veterinarian.