He was competing in a one-star class event on The Drover when his horse tripped at a fence yesterday afternoon (British time).
Amanda Redditt said Mr Gadsby first came into her life as a 13-year-old who desperately wanted a pony.
"I gladly gave you Muffy & watched the both of you learning together & you having so much fun with her," she wrote.
"I was honoured to have known you as a friend, you had a heart of gold and a huge personality to match. It is such a waste to lose not only such a hugely talented rider but a truly lovely person as well."
Natalie Fraider said Mr Gadsby was "the most wonderful person".
"We have lost a part of our heart today but you gave us such wonderful memories to hold onto forever. You even started a tradition of 'Bubbles Nights' and we will celebrate your life with one. Love you always Tom. My heartfelt sympathy goes out to your family."
Nicholas Fyffe said his life was "swiftly put into perspective" when he heard of the rider's death.
"My thoughts go out to his family having lost him so young. Such devastating news for the equestrian community worldwide. May he rest in peace."
Equestrian Sports New Zealand (ESNZ) chief executive Jim Ellis said the sport was deeply saddened.
"On behalf of ESNZ members I express our sincerest condolences to Tom's family and close friends," he said. "Tom was a talented showjumper and eventer who was in Europe to fulfil his dream of competing as a professional event rider - a dream he achieved but which has been tragically cut short."
He thanked colleagues at British Eventing, their officials and medical staff who did everything possible for Mr Gadsby after his fall.
British Eventing chief executive Mike Etherington-Smith said everyone was saddened and shocked.
"Our thoughts and prayers are with Tom's family at this really sad time."
Mr Gadsby, from Kerikeri, had been competing in Britain since last year and was based near Huntingdon in Cambridgeshire.
British Eventing, ESNZ and the International Equestrian Federation will investigate the incident.
