It depends on the horse. Most are fine without a blanket. Older horses, those with less body fat, etc may need one sooner. If your horse is wet or shivering, blanket him. Normally though, like Kevin said, most will do fine without one.
We usually blanket our horses between -30 and -50 degrees and feed them lots, but a good way to judge is wether they are shivering... If they are give them lots of extra hay, if they are still cold blanket them, you can even double blanket them if you have to... It really depends on where you live. I live in alaska so our conditions might be a little bit different than yours.
Its not so much to do with the temperature as it is the WIND.
It can be -25F and calm, the horses will be just fine here. However if it was 10F and super windy, I have a few who will be pretty cold and need a blanket. Lucky for me I live in the woods, no wind and plenty of natural shelter.
Age and condition of the horse has a lot to do with it. Also the shelter that they have access to. If you have a barn with single stalls then they are out of the wind and rain and can manage on their own....again you would need to factor the condition of the horse. If the horse is old or very malnourished then it can't sustain it's own heat, so blanket them. If your horse is in good condition and at a good weight and he has a shelter (even a lean-to) then he should be ok.
IMHO, the best thing that you can do for a horse in winter is make sure that they have access to plenty of forage (grass hay/alfalfa/etc). A horse's digestive tract generates a good portion of their body heat so a horse with no blanket and constant access to forage will generally be better off than a blanketed horse who is being fed only grain or is only being fed 1 time per day. Though the winters don't generally stay really cold here, there are nights that it gets colder than -10 degrees, many times with a wind chill that is even colder. My horses are outside 24/7 and none have ever been blanketed. Never had a problem with a horse being too cold.
It really depends on the horse and what they are doing. My horse is in training 365 days out of the year and it can nip down to -50C here. He grows a winter coat, but I shave it off so he is more comfortable in his workouts. Because of this, he is blanketed heavily throughout the winter months. Below about 10C I blanket him, and he has a fly sheet on during the summer to keep him blacker.
For him I have about 7-8 blankets (omg that's absurd!) I have 3 weights of winter blankets, one with a hood, two weights of stall blankets, a sheet, a rain sheet and a fly sheet.
However, for my mother's horse who is for pleasure, he has a nice wooly coat and no blanket in the stall, he has one winter blanket and a rain sheet and that's it! Last year he was outside 24/7 un-blanketed and came out of the winter fat and happy.