The company operates the Snow Park business on land owned in the Cardrona Valley by the Lee family.
Mr Lee is the son of Cardrona skifield entrepreneurs John and Mary Lee. He announced his resignation in a press release and declined comment.
Mr Synnott also refused to comment. Mr Lee founded the Snow Park in 2001 and has been involved in its management since then.
"I am extremely proud of the reputation and standing Snow Park has achieved on a local, national and international basis," the press release said. "I have come to the decision to resign following advice received from my lawyer. I have been having difficulties in serving the best interests of the company due to the deterioration of my professional relationship with my former fellow directors and shareholders, the Synnotts.
"It has become apparent that we have a difference in values and I feel my role as operations manager and my ability to serve the day-to-day needs of the company have been compromised. I am leaving the company in good heart and good hands as the team that has been assembled for the forthcoming season is second to none. I remain as a shareholder in the company."
Snow Park Holdings Ltd was incorporated in March last year with Mr Lee and Robin Sadowski-Synnott as directors.
Mr Lee is 50% shareholder, as is the Synnotts' company, Alpine Ventures 2010 Ltd.
The Synnotts took responsibility for customer services, hospitality, strategic direction and financial administration, while Mr Lee was the terrain park's day-to-day manager.
The Synnotts' investment has been reported to include a stake in future developments John Lee has been pursuing for many years, such as an approved but unbuilt $19 million gondola and the proposed Roaring Meg Resort.
Landowners John and Mary Lee founded Cardrona Alpine Resort in the 1970s and sold it in 1989 so they could develop Waiorau Station on the Pisa Range.
John Lee (75) has stated he wants to retire but is keen to see a succession plan in place to secure his dream of developing the Roaring Meg skifield.
The Lees sold their vehicle proving-ground business in 2004.
Last year, they put Waiorau Station on the market but could not find a buyer. However, they hope to settle a contract to transfer the Snow Farm cross-country ski facility to a charitable trust later this year.
Mr and Mrs Synnott have lived at Lake Hawea for three years and have five children. Auckland-born Mr Synnott grew up at Manapouri and Mrs Synnott is from New York. They have had careers in finance, marketing and computer information systems.
