Police were notified at about 7:45 a.m.
"We are currently investigating whether it is an exposure death or if something else is going on," Farmington police Lt. Taft Tracy said.
The man had not been identified Tuesday evening.
It appeared the man walked to the west of the park on a trail. The trail goes under the bridge and opens up to an area of river rocks that lead to the ice where his body was found.
Though the investigation is ongoing, it appears the death is related to spending a night outside in cold temperatures, Tracy said.
The overnight low on Tuesday was 5 degrees, which is 15 degrees below Farmington's 30-year-average, said Tim Shy, the senior forecaster for the National Weather Service in Albuquerque.
Colder than usual temperatures have settled in northwest New Mexico since Dec. 8, Shy said. That was when a cold air mass from northwest Canada first crept into New Mexico.
"The key message is when temperatures get this cold somebody outside should not underestimate the importance of warm clothing," Shy said.
It was the second person who has been found dead this winter in Farmington after a night outside, Tracy said. The first death was in December.
Tracy said the public has been helpful in reporting people who are outside, and appear at risk.
Police are mindful of the dangers of cold weather.
Officers "actively keep a lookout for this," he said. "If we locate them and they are out and about and look at risk we will make contact and check on their condition."