HARBOR SPRINGS, Mich. — Wearing neither coat nor shoes, a fugitive suspected of killing and dismembering his wife was found hiding under a fallen tree yesterday in a snowbound state park after a bitterly cold night on the run, authorities said.

Police tracked down Stephen Grant about 225 miles north of the suburban Detroit community where body parts believed to be those of his wife were discovered. He was in stable condition and was being treated for frostbite and hypothermia under police guard at a hospital.

Mr. Grant was wearing only slacks, a shirt, and socks when he was captured nearly 10 hours after he abandoned a truck and set out on foot in Wilderness State Park near the tip of Michigan’s Lower Peninsula, Emmet County Sheriff Pete Wallin said.

He had no weapons and did not resist.

“I don’t think he probably could have made it much longer in those kind of conditions,” Mr. Wallin said during a news conference. “I wouldn’t want to be out there unless I was dressed for it.”

Mr. Grant, 37, will be returned to Macomb County for arraignment in the death of Tara Lynn Grant, a 34-year-old businesswoman and mother of two who disappeared last month.

A torso found in the family home and other body parts found in a park near their home were believed to be hers.

Tara Grant last was seen February 9, and police said the couple had argued that day over her business travels abroad. Her husband reported her missing five days later; he has steadfastly maintained his innocence.

Macomb County Sheriff Mark Hackel said Stephen Grant fled in a friend’s pickup Friday hours after police executed a search warrant on the home in Washington Township.

Deputies traced calls from his cell phone and a withdrawal from an automatic teller machine, Mr. Wallin said.

After finding the truck just south of the isolated Lake Michigan park, police with a tracking dog searched on foot and snowmobile, aided by a Coast Guard helicopter.

They pounded on doors and warned occupants of nearby homes and the handful of cabins inside the park.

“We didn’t know what we were up against,” Mr. Wallin said. “We knew he was suicidal, we knew he could be armed and dangerous.”

The helicopter crew, dispatched from the U.S. Coast Guard station in Traverse City, spotted fresh footprints in the snow and guided ground searchers in Grant’s direction, Lieutenant Jeremy Loeb said.

“We could see where he’d lay down, get up, lay down again,” Mr. Wallin said.

After an all-night search, he was found about 6:30 a.m. near Big Sucker Creek, which flows into Lake Michigan, about three miles from where he abandoned the truck, authorities said.