The family took off Dec. 22 in a single-engine plane from Loveland, Colo., headed to Jackson, he said.
The plane, a 1998 Commander AC 11, crashed about 15 to 20 miles southwest of Lander, near Christina Lake, at an elevation of about 11,700 feet, said Allen Kenitzer, a spokesman for the Federal Aviation Administration.
McAuslan and Kenitzer said their agencies don't have any word yet on the cause of the crash. The National Transportation Safety Board was investigating.
A plane in October also crashed during a snowstorm in the Wind River Range. It took searchers several days to find the bodies of Minneapolis pilot Luke Bucklin and three of his sons.
"I think it would be probably inexperience with mountain terrain in Wyoming," McAuslan said of the recent plane wrecks. "It seems to me that if you're going to fly to Jackson, there are probably a lot better ways to go than crossing the highest point in Wyoming."
McAuslan said Day's plane hit the top of a ridge, in a steep area where the snow was perhaps 3 feet deep. He said he was not certain what the weather conditions were in the area at the time of the crash.
Kenitzer said preliminary information showed Day had not filed a flight plan. McAuslan said local authorities weren't aware that a plane was missing in the area until they received the report of the locator beacon.
A helicopter transported a team to the site on Saturday and removed the bodies, McAuslan said. He said autopsy on the pilot is pending.
Radio station KJAS in Jasper, Texas, reported Day and his wife owned and operated a business called Day Forestry Appraisal and Management Co. in that city. The family apparently left Jasper on Tuesday and made their first stop in Colorado, KJAS reported.
They had planned to visit Yellowstone National Park and then travel to Alaska.
Kenitzer said the plane was registered to the Condor Aero Co., a limited liability company in Jasper.