Spaying is performed with the mare standing in stocks, sedated and given an epidural. The surgery itself is fairly fast, the vet goes in rectually, finds the overies and then a slit is made in the rectum, the overies are brought through the hole and then removed after the blood vessels have been crushed with a special instrument called an ecalasiur(sp). Yes, there are risks of bleeding if a major vessel is cut which can happen, although very rarely and that means almost instant bleed out and death. I have heard of it happening one time in all the years I have known about spaying and helping in surgeries. We do them in the winter since the mare is out of heat and the overies are small.
The mare is kept standing in a stall for 48 hours so she won't lay down and roll until the internal incisions are healed. Then pretty much normal every day routine, but most vets suggest no riding for about 3 weeks. I have had four mares done now and love the results.
We do the surgery here in Wyoming for about $600 which includes surgery, hospital time, meds etc. Then you take them home and have to give more antibiotics for three weeks or so, so that is extra. Not much if you don't want to deal with heats or accidental breedings, etc.