The European individual eventing champion, 45, fell from her horse JL Dublin 10 days ago.
A statement posted on her official website read: “Nicola is at Southmead Hospital in Bristol following her fall from JL Dublin at Badminton Horse Trials on Saturday 7th May.
She remains comfortable and in good spirits.
Nicola Wilson statement
“Nic is still in intensive care, and is expected to remain there for the next week to 10 days before being moved to a spinal unit closer to home.
“She remains comfortable and in good spirits.
“‘Dubs’ (JL Dublin) is happy and content, and is enjoying the sunshine and the spring grass.”
British Equestrian said last week that Wilson had suffered “several spinal fractures” but did not require surgery.
Wilson, who is from Northallerton in North Yorkshire, won European individual and team gold aboard JL Dublin in Switzerland last year.
She was also a member of Great Britain’s silver medal-winning team at the London 2012 Olympics.
Badminton cross-country action was watched by a crowd of more than 100,000 as the event returned following a three-year absence.
Laura Collett and London 52 claimed a first Badminton win, with world champion Ros Canter finishing second and Collett’s Tokyo Olympics team gold medal-winning colleague Oliver Townend taking third.