WASHINGTON — The trees in the capital are barren, spindly things. The temperature has dipped, requiring puffy coats. With the government open — for now — President Trump has left the frigidity of governing for a weekend in Palm Beach.

But in a town where not even the longtime operation of the federal government seems certain, Mr. Trump has adhered to one constant: a conspicuously sun-kissed glow, one that has shone like a stoplight against Washington’s graying backdrop. Much like Warhol’s shock of white hair or Big Bird’s saffron plumage, the president’s vibrant hue is so consistently present and meticulously maintained that it was a culturally embedded representation of him long before he entered politics.

The president’s shade is one that Alec Baldwin, the actor who portrays Mr. Trump regularly on “Saturday Night Live,” recently described as vacillating between a “Mark Rothko orange” and a “slightly paler Orange Crush,” depending on the setting. Which right now is February in Washington.

“Which is not in the tropics last I checked,” Mr. Baldwin said in an interview.

The official line from the White House, as with other matters surrounding the president’s physical health and appearance, is that Mr. Trump’s glow is the result of “good genes,” according to a senior administration official who would speak only on the condition of anonymity.

And, O.K., a little powder — a translucent one, not a bronzer — which the president applies himself before television appearances, the official said.

But mysteries abound. One persistent question: Does Mr. Trump use a tanning bed, as a talkative makeup artist said in 2016 and Omarosa Manigault Newman, a former aide, claimed in a tell-all book? (Ms. Manigault Newman wrote that an usher was fired for mishandling transport of the contraption.)

Mr. Trump’s former boarding school classmates have described him as a fan of ultraviolet rays, someone who would pop a tanning bulb into a light socket to go “to the beach.” Even James B. Comey, the former F.B.I. director turned presidential foe, speculated on Mr. Trump’s glow. The president’s “face appeared slightly orange,” Mr. Comey wrote in his memoir, “with bright white half-moons under his eyes where I assumed he placed small tanning goggles.”

But according to three people who have spent time in the White House residence, no such bed or spray-tan booth exists in a hidden nook of the residence, a cranny of the East Wing or a closet on Air Force One. Two senior White House officials insisted that no such apparatus exists.

Several of the president’s supporters had little to say when asked how the president achieves his glow or other ways in which he prepares to get camera-ready. One former campaign hand admitted that aspects of the president’s process sound “like a captivating story” but declined to elaborate, saying that Mr. Trump should be allowed to get dressed in peace.

“He looks more orangy than he does tan,” a telltale sign, Dr. Alster said.

Another sign — and one that would rule out dietary supplements or medicines that give skin an overall tan, Dr. Alster added — is the sight of the often-present white circles under Mr. Trump’s eyes when he goes before the public.

“There have been enough people that have asked me in his orbit,” though not on the president’s behalf, to see what Mr. Trump could do to achieve a more even skin tone, Dr. Alster said. “I have nothing against self-action tanning creams, but I think you need to be careful about how you apply it.”

She added that Mr. Trump’s skin appears to show past sun damage, and praised him for breaking any former tanning bed habits.

Certainly Mr. Trump, who has long taken antibiotics to treat rosacea, a condition that can make the skin appear rosy and ruddy, is attentive to how he looks on television. He has complained that his skin and hair appear too yellow or orange on the screen, according to one person familiar with his views.

As a result, events in the White House are now more dimly lit than in previous administrations. The president has also become a fan of natural light, like the setting of the White House Rose Garden, where Mr. Trump chose to announce the end of the government shutdown in 40-degree weather.

Whatever Mr. Trump may do or not do to his skin, he does it in private. A taxpayer-funded White House makeup artist has volunteered her services, but she has not gotten close enough to try, according to two people who have overheard such discussions. A half-dozen current and former aides and people close to Mr. Trump say he has long been self-sufficient in matters of grooming.