Arriving at the world famous theme park in plastic ponchos, the MacDonald family, from Scotland, was relaxed and ready to "get a few hours in" before riding out the storm at their hotel.

"We're not worried, we've got water" stored up, said Emma MacDonald, 51, making her second trip to Disney in a decade.

Just a few days into their two-week vacation, she told AFP they were not disappointed with the situation. "Just nothing you can do," she said.

She said the number of evacuees staying at their hotel who fled Florida's west coast, which is expected to be pounded by a Category 4 Milton overnight, put the situation into perspective: "It's them we feel sorry for."

The family was among dozens arriving at Disney -- some 60 miles (95 kilometers) inland from Florida's west coast -- under covered skies, with alternating light and heavy rain.

Only a few hundred cars were in the parking area about an hour after opening time, and buses from hotels around the resort were arriving mostly empty.

But a full contingent of workers was out and ready to screen and move the crowd on their way into the park.

Disney, the state's largest employer, said it would close at 2:00 PM on Wednesday and possibly remain shut down on Thursday, depending on the storm damage.

But the hotels will remain open, harboring thousands of evacuees as well as tourists on long-planned vacations.

That includes Linsday Moore, 42, who arrived on Sunday all the way from Maui, in the US state of Hawaii.

"We thought about canceling but (our) airlines wouldn't let us" at the time they were heading out, she told AFP, with her husband and young child by her side.

She said they've experienced heavy storms living in the Pacific, so they knew what to expect.

"They say this area (Disney) is the safest for these storms," she said, also acknowledging that their situation was not comparable to the evacuees staying in their hotel.

Asked about heading into the park just ahead of the storm, she said: "It's safe and we're here, so might as well."

Jennifer Lizcano, 77, was also trying to make the most of her trip from San Diego with her daughter Rose, 44.

She said she was excited to experience the often crowded park with so few others -- a rarity that one vlogger also entering Disney was preparing to document.

Before going through security, Lizcano said that though the storm was on its way, "we're not there yet!"