Thank you for asking this question! We don't get enough ones about women and their daily lives. Also, thank you for using the term "squad picnic" in a Victorian context. I just want to share a couple of lovely related images: "The Holyday", by James Tissot, ca. 1876, and "At the Seashore", by Luigi Lior, ca. 1880.

Nineteenth-century women did not need to be constantly chaperoned by men, but chaperonage was an issue for certain women, depending on how broadly you're defining "women" - the main focus of chaperonage was on teenagers, whose "unassailable purity" was of intense interest even relatively far down the social scale. For roughly the first two-thirds of the century, American standards were much laxer than those in Europe, but it gradually became more common and expected for American daughters to be actively watched, perhaps as a result of greater amounts of Americans traveling abroad. In America, the daughters of recent immigrants continued to be under more parental restrictions and watched more strictly than those of the native-born/assimilated well into the twentieth century. It was not just enough for a young, unmarried woman to be a virgin: she had to have a good reputation among her society as the kind of girl who was of course a virgin, without any episodes of behavior that might leave her open to comment (e.g. being seen in a secluded spot alone with a boy). However, the chaperone was traditionally a woman, either married or old enough that she'd attained "matron" status without actually having been a wife/mother. In some circumstances, she was a relative of the girl being chaperoned, but in others she might be the hostess of an event or an older woman invited to be a member of the party - there didn't have to be a strict one-to-one ratio of girls/chaperones, there just had to be at least one "supervisor".

Picnics and other outdoor activities were actually typically seen as good opportunities for relatively unsupervised male-female interaction, but there was no reason why they couldn't be done homosocially. For girls, this would still mean a female chaperone to make sure they weren't behaving poorly or meeting up with young men (boys on a formal picnic/trip would typically also have a chaperone to make sure they weren't doing dangerous things, vandalism, etc., though informal time spent together was unchaperoned), but adults could do what they liked.

Women and girls certainly did have friends that they spent time with away from men! The well-known and very common practice of "paying calls" was not solely feminine, but in effect any woman paying the calls or staying at home to wait for them was spending the day with other women more than with men, for instance. Linking arms and holding hands was also done homosocially by both men and women. As I sort of touch on in my previous answer regarding male emotionality, the end of the nineteenth century saw a greater amount of attention paid to the concept of homosexuality, leading to a solidification of many of the "anti-effeminate" norms of masculinity that we have today, such as the idea that men should avoid touching each other gently; at the same time, there was a flowering of literature about "romantic friendships" between women that only tapered off after the turn of the century. If you really want to read about intense female relationships that have nothing to do with men, I'd definitely advise looking into that concept!

(I feel like this is on the short side given the scope of your question, so please do ask if you have any further questions.)

"The Perfect Comrade: Why the Girls Need Chaperonage", Good Housekeeping (1908)

"When is Chaperonage Required?", Social Observance: A Series of Essays on Practical Etiquette (1896)

"Nebulae", The Galaxy (1877)

Carolyn W. de la L. Oulton, Romantic Friendship in Victorian Literature (Routledge, 2016)

Vicki L. Ruiz, "The Flapper and the Chaperone", Delinquents and Debutantes: Twentieth-Century American Girls' Cultures (NYU Press, 1998)

Cas Wouters, Sex and Manners: Female Emancipation in the West 1890 - 2000 (SAGE, 2004)

You need to specify a country or culture- things varied a lot depending on where you lived.