This is a very common question and the answer has more to do with your particular situation than just the recommended times of year. If your horse lives in a dense horse population such as a stable with common pasture, then I recommend deworming 4 times per year. If your horse lives at home with just a couple (2-3) other horses, then every 6 months is appropriate +/- a deworming during the summer months (May thru Sept). In extremely high density situation, >10 horses per acre of pasture or performance show barns with multiple horses coming and going on a weekly basis, I recommend every two months during the summer months and then every 3 months during the winter months.
It all has to do with herd immunity and contact with potential sources. If your horse is more likely to be incontact with multiple horses of unknown vaccination and deworming status, then you need to take additional precautions to vaccinate and deworm them. See where your horse fits into this scale and deworm appropriately. If I were to be technical about deworming, most parasitic worms only need 3 weeks to begin repopulating the colon following a dewormer. Obviously, there is rarely ever any need to deworm this often. Good management practices such as cleaning manure from feeds or breaking it up with a harrow to expose it to the sunlight will also decrease the likelihood of your horse coming in contact with contaminated manure. Hope this answers your question. Best of luck.