Bob Hope and Dolly Parton strolled arm and arm down the path, bundled up in wool and fur as the snowflakes fell and their voices joined in "Silver Bells."

But this was a white Christmas, show biz style.The stars must have been hot as the dickens because the scene was being shot at Williams Island, Fla., as the temperature eased off from an earlier 80-degree high.

The "snow" was a combination of shredded Styrofoam and cotton, being dropped from a big wooden box suspended among the palm trees by a giant crane.

Hope and Parton weren't even really singing - they were lip sync-ing to a pretaped song.

But it will look like an honest-to-Santa snow scene when Bob Hope's Jolly Christmas Show (7 p.m., Ch. 2).

The show was taped at Williams Island, a lush condo resort that boasts Sophia Loren as its resident spokesperson, and aboard the new luxury cruise ship, the Royal Viking Sun, anchored at the Port of Miami after her maiden Atlantic crossing.

Hope tried out portions of his monologue, always a high point of the show, both on the island and aboard the ship. Politics, as always, played a major role, and among the jokes were:

- "This was Reagan and Gorbachev's fifth meeting - that's three more than Bush and Quayle."

- Santa is bringing "a gold watch for Bush and a set of trains for Quayle."

- The meeting in New York of Gorbachev, Reagan and Bush was "Georgie, Gorby and the Gipper."

- Raisa on her visit to Bloomingdales: "In the Soviet Union we don't train women for combat."

- The State Department refused to let Yasser Arafat come to New York because it was worried about terrorism. "What the heck - if he gets mugged, he gets mugged."

- Bush has vowed, "After my inauguration, I'll never eat another jelly bean again as long as I live."

- Bush's tough new personality has hurt attendance at libraries: "They're staying home and reading his lips."

- There will be the patter of little feet in the White House now, but Michael Dukakis is disappointed. "He hoped they'd be his."

- "George Bush knows a lot about defense - he was ready to defend Pearl Harbor three months before it was attacked."

In a relaxed moment between tapings, Hope spoke admiringly of Bush and Dan Quayle - but he will needle them as he does every administration. He reminisced about golfing with Eisenhower - and joking about Ike's golf game.

Then there was the time in 1962 when Hope's son graduated from Georgetown University in Washington and Hope did some jokes about President Kennedy, who he said "was one of my favorite guys."

"The next day (presidential press secretary) Pierre Salinger called me at my hotel and said, `The boss wants to see you,"' Hope said. "I went over to the White House and I sat there for an hour-and-a-half telling jokes."

As for Quayle, a natural target, Hope said:

"I think he's going to make a good vice president. What the hell is wrong with 41? I remember 41. It was fun."

He couldn't resist a gag about "the all-important grade school vote," but added, "I think it's great to have a young guy in there. You can't have everybody in the cabinet on Geritol."

The show includes a brief chat with Don Johnson, skits with Dodger pitcher Orel Hershiser and Olympic track star Florence Griffith Joyner, and a number in which Hope and Parton wear reindeer suits.

At one point the shot was ruined because their reindeer antlers tangled and Dolly cracked up the crew by ad-libbing, "We're both too horny."

Hope, Parton and the two athletes did a number together titled "It's Not Where You Start - It's Where You Finish," which proved that Hershiser has a Good singing voice and Flo-Jo looks gorgeous.