- Nicholson, 54, one of eventing's most successful riders
- He suffered injuries at cross-country event
- Surgeons at Oxford operated on him for eight hours
Nicholson, 54, was rushed to hospital after the accident, which happened at the final fence of a cross-country event in Gloucestershire 11 days ago.
His horse, Cillnabradden Evo, was unhurt.
Nicholson, one of eventing's most successful ever riders, underwent an eight-hour operation at the John Radcliffe Hospital in Oxford.
The New Zealander told reporters on Thursday: "My surgeon, Mr Jeremy Reynolds, told me the injury I sustained to my neck would have caused paralysis at the time of injury in 98% of cases.
"I realize I have been incredibly lucky. I underwent an eight-hour operation where they repaired the fractures and stabilized my cervical spine.
"This procedure in itself was not without risk, and I cannot thank the team of spinal surgeons enough for what they have done."
He said he did not know when he would be able to make a return to competition, and added: "While I have to take things easy, I am up and about and fully mobile and I look forward to getting back to full fitness in due course.
"I want to take the opportunity to thank everyone for their kind messages and support, which have meant a lot to me and my family."
Nicholson has won three Olympic team medals with New Zealand, including bronze at London 2012, has three World Championship medals and is a five-time winner at the Burghley Horse Trials.