Two different legal cases offer guidance on when singing jurors are considered grounds for a new trial, and when they're not.
Details from the Virginia Law Register - April 1905.
WHEN THEY'RE NOT:
Where the jurors after retiring to consider of their verdict attempted to sing and one of them was unable to carry the "base," it is not ground for a new trial that a man who was not a member of the jury joined them and gave them "the proper air."
From the case
Collier v. State
WHEN THEY ARE:
It is a ground for a new trial that the jury in a murder case upon retiring went to a hotel, got drunk, and in coming up to their room in the hotel sang "We are climbing up the golden stairs."
From the case
State v Demareste La
This was legal???

Macon Chronicle-Herald - Sep 8, 1989
Apparently so. Some googling reveals that this situation seems to happen fairly regularly.
Most recently, there was the case of Judge Thomas Ensor of Colorado whose wife served as a juror in his court. During the trial the judge repeatedly cracked jokes about the presence of his wife, such as, "Be nice to Juror 25. My dinner is on the line."
Inevitably the case was appealed, but in June 2020 the Colorado Supreme Court ruled that it was legal for Ensor's wife to be on the jury, noting that the defense lawyer could have objected to her sitting as a juror, but didn't. (Though the defense lawyer had said that he was afraid to challenge her.)
More info:
ABA Journal
The ad below, in which trial lawyer Melvin Belli endorsed Glenfiddich scotch, ran in the
New York Times and
New York Magazine in early 1970. Taken at face value, it doesn't seem like a particularly noteworthy ad. However, it occupies a curious place in legal history.
Before the 1970s, it was illegal for lawyers to advertise their services. So when Belli appeared in this ad, the California State Bar decided he had run afoul of this law — even though he hadn't directly advertised his services. It suspended his license for a year. The California Supreme Court later lowered this to a 30-day suspension — but it didn't dismiss the punishment entirely.
Some high-placed judges felt sympathetic to Belli, which added fuel to the movement to end the 'no advertising' law for lawyers, and by 1977, the Supreme Court had struck down the ban on advertising, saying that it violated the First Amendment. That's why ads for legal services now appear all over the place. Compared to the ads one sees nowadays, Belli's scotch endorsement really seems like no big deal at all.
More info:
Belli v. State Bar,
"Remember when lawyers couldn't advertise?"

New York Magazine - Mar 2, 1970
Photo source:
The Baltimore Sun Baltimore, Maryland 21 Aug 1953, Fri • Page 4
Text source:
Los Angeles Evening Citizen News (Hollywood, California) 21 Aug 1953, Fri Page 11
I would totally cite this precedent when trying to get out of jury duty.
Source:
The Atlanta Constitution (Atlanta, Georgia) 26 Jan 1909, Tue Page 9
English eccentric Henry Budd stipulated in his will that his sons would forfeit their inheritance if they ever grew a mustache.
Details from twickenhampark.co.uk:
Henry lived until 1862 when he died in London. In his Will his estate was valued £200,000 which would be tens of millions today. The Will divided his estates between his only surviving children, namely his sons William and Edward. Henry added a final stipulation that should either of his sons grow a moustache they would forfeit their share which would revert to the other brother.
The newspapers reported this in some detail at the time, and it was still worthy of news 20 years later in 1882.

Detail from Budd's will in which he forbids his sons from ever growing mustaches
Various sources report that when Madame de la Bresse died in 1876, she instructed in her will that all her money be used for buying clothes for snowmen. For instance, Bill Bryson shares this anecdote in his 1990 book
The Mother Tongue: English & How it got that Way:
[The nineteenth century] was an age when sensibilities grew so delicate that one lady was reported to have dressed her goldfish in miniature suits for the sake of propriety and a certain Madame de la Bresse left her fortune to provide clothing for the snowmen of Paris.
Here's a 1955 cartoon about Madame de la Bresse and the snowmen:

The Montana Standard - May 6, 1955
But the earliest source for the story I've been able to find is a 1934 edition of Ripley's
Believe it Or Not!. Which makes me wonder if the story is true, because I'm convinced Ripley invented many of his "strange facts". I can't find any French references to Madame de la Bresse.
However, it's possible Madame de la Bresse and her odd bequest were real, and the best argument for this I've been able to find is made by Bob Eckstein in his
The History of the Snowman. He doesn't provide any sources to verify the existence of Madame de la Bresse, but he does give some historical context that could explain what might have inspired her to want to clothe snowmen:
When noted prude Madame de la Bresse passed away in 1876, she instructed in her will that all 125,000 francs (about $22,500 today) of her fortune were to only be spent putting clothes on the vulgar and offensive naked snowmen in the streets. This bizarre bequest may have had something to do with a certain celebrated snow statue made during the later part of her life in 1870...
The date was December 8, 1870. Snow began to cover Paris. Bored officers threw snowballs, and some of the soldier-artists began to make snow sculptures. Before long, the snowballs became monumental snow statues. One soldier, Alexandre Falguière, channeled his angst of his home city being attacked by creating La Résistance, a colossal snow woman, which was constructed in a mere two to three hours with the help of others.
Although the artist Moulin built a huge snow-bust nearby, it was twenty-nine-year-old Falguière's snow woman that attracted the press to visit the site...
The snow woman was light in the bosom yet clearly blessed with a female face. She had broad shoulders with folded muscular arms and possessed an able-bodied, World Wrestling Federation savoir faire, which suggests Falguière compared the Prussian siege of Paris with the sexual aggression of a relentless female refusing to succumb (La Résistance).

La Résistance by Falguière. Source: wikipedia
So maybe Madame de la Bresse was invented by Ripley. Or maybe she was real and decided to clothe snowmen because she was offended by Falguière's nude snow statue. I'm not sure. Hopefully someone else may be able to shed some light on this mystery!