Even winter-weather-loving businesses are succumbing to the extreme cold locked down on Minnesota this week.

Across the state, ski slopes that usually draw crowds shut down Monday, as did a covered tennis dome in Minneapolis.

Some stores that could provide a cozy shopping diversion on chilly days also shut their doors. Even pizza shops dealt with a paradox of the extreme cold: lots of delivery demand but few diners at the tables in the restaurant.

And business owners statewide braced for yet another rough day on Tuesday, when the high isn’t expected to surpass zero in the metro area and windchills are expected to be as low as -40. Modest relief is expected late Tuesday and Wednesday, but temps will remain well below freezing.

Still, in a variety of ways, businesses coped. Some that didn’t shut their doors kept limited hours, or sent some employees home, or offered discounts.

From Buck Hill in Burnsville to Welch Village in Goodhue County to Giants Ridge in Biwabik to Spirit Mountain in Duluth, most ski slopes closed, done in by deadly windchills. At least one, Afton Alps, planned to reopen at 3 p.m. Tuesday

So did the indoor Reed-Sweatt Family Tennis Center on Nicollet Avenue S. in Minneapolis, which closed Monday.

Don McClure, general manager at Buck Hill, said that even if the place were open, no one would be there. “When it’s this bitter cold, people select other options,” he said, mentioning movies and video games as alternatives.

Still, McClure said he isn’t worried about business in general because, he said, extreme cold builds demand. “When we hit 35 degrees, we just blow the doors out,” he said. “The big days are making up for it.”

On St. Paul’s pedestrian-oriented Grand Avenue and at other locations, the Bibelot gift shop closed. “It’s a hardship for people to get out,” Bibelot owner Roxy Freese said. “We didn’t want to put our employees through that.”

She contemplated opening for a few hours but decided against it, saying, “This is very unusual. I hope my customers understand.”

Marie Dwyer, co-owner of Cooks of Crocus Hill in St. Paul, Edina and Stillwater, sent out an e-mail offering customers 20 percent off purchases in the store or online. “It’s to drive traffic and interest and give people a break,” she said.

Independent stores struggled to balance the need to maintain consistent hours with the lack of revenue and safety concerns that extremely cold days can bring, and not all made the same decision.

A la Mode Boutique & Nail Salon at 50th and France in Edina stayed open. “We want to be here for clients,” owner Sara Saferstein said. “We can’t keep closing when it’s cold.”

Floyd’s Auto Sales in Stillwater was open, too. Manager Sharon Jensen said January sales fluctuate, but the volume of customers is down by about half this month.

“I’m certainly hoping for warmer weather,” she said. “It always works out; you’ve got to keep a positive attitude.”

Knowing your customer

At Pizza Lucè in Duluth, the cold gives and takes — deliveries spike, but fewer customers come to the dining room. Delivery manager Alex Eklund said cold streaks have a flow in the pizza business — the beginning of a cold streak sends deliveries soaring, but as the cold wears on, stir-craziness sets in and people need to get out — unless it gets too cold.

“As Minnesotans, we get used to the 10-below,” Eklund said. “But 20-, 30-below — anybody gets cold.”

As the temperature drops, discounts get deeper at Sebastian Joe’s, the Uptown coffee-bakery-ice cream shop. Ice cream was going for 25 percent off Monday.

“People know about that discount, so they’ll come in for that. There’s a lot of die-hard ice cream eaters,” bakery manager Tamra Leoni said.

Leoni works the early shift, baking the gooey goods, then greeting coffee customers. “People on their way to work, they still need their coffee,” she said, adding that the scent of warm baked goods probably helps them keep coming.

Warmer days are busier at the Downtowner Car Wash in St. Paul, but general manager Steve Plisek said extreme cold actually is a great time to wash a car, because slop won’t splash up from the frozen-over roadways. “Your car will stay cleaner longer,” he said.

Car doors and locks get extra treatment at the Downtowner, treated with lubricant and de-icers. On Monday, he saw a steady flow of cars and was operating three of five cleaning bays.

If you can, stay inside

The pride of acclimation notwithstanding, caution should prevail.

Dr. Anne Lambert, co-director of Hennepin County Medical Center’s burn unit, said dressing for extreme cold means layers, facemasks, mittens (not gloves) and woolen socks. The burn unit normally admits 30 patients per season with severe frostbite. So far this month, the unit has admitted about 90, she said.

“I can’t stress enough how important it is that people stay home,” she said. “If you don’t need to go outside, you shouldn’t.”