Horses, like goats and most breeds of sheep are seasonal breeders. They are affected by the length of daylight. I believe the term is 'polyestrus', but all my livestock books are upstairs and I don't feel like running up to get them at the moment.
Anyhow, a mare will only cycle naturally in the spring/summer/fall months, and the first two or three heats and the last two or three are not regular, so it's not a good idea to breed your mare during those times. Gestation is roughly 11 months, so you breed your mare a month later than the month you want her to foal (you want a June foal, you breed in July).
The people who have foals born in January/February have usually had to put their mares under artificial light to keep them cycling throughout the winter. Racehorse people usually have the funds/facilities to do this, the normal horseperson does not.
Fern, you are correct, though again, this is usually with Racehorse people (and might be an outdated practice, but I don't know). At one point January 1st was the birthdate that all registered Thoroughbreds got. I believe it was the same with the Standardbreds.