(This post started with a Dorian/Vivienne crochet/knitting rivalry headcanon, and got out of hand from there).
Dorian crochets. Back in Tevinter he had a lady friend who tried to teach him to knit, but he never got the hang of it and has felt bitter toward the craft ever since. On the ship from Tevinter, however, he encountered an elderly woman who taught him to crochet to help keep his mind off his seasickness. Is constantly making little gifts for the other members of the Inquisition, mostly hats and scarves and such. Bickers with Vivienne about whether crochet is better than knitting, but they still get each other yarn for holiday gifts. Dorian likes soft yarns in bright colors.
Vivienne knits. It helps focus the mind and is not unlike spellcasting in many ways. She makes intricate, lacy things using the tiniest needles and the finest thread. She only gives things away to her closest friends, and one considers it a great honor to receive a shawl from Madame de Fer; the Iron Bull has a scarf that he is very careful with.
At one point Vivienne and Dorian are engaged in a very heated debate that is full of arcane technical language, and the Inquisitor asks Solas “Are they talking about magic again?” to which Solas replies “No. Knitting. Or crochet. I can never remember which is which. They’re basically the same anyway.” At which point both parties turn on him to explain in great detail exactly what the difference is. Solas himself cannot knit; his socks have been darned a million times because he doesn’t know how to make new ones.
Sera’s journal has that note about wanting to learn to knit; it’s “like stabby sewing.” She badgers Vivienne into teaching her, and Vivienne tries, but well, it’s Sera. Soon her loft is littered with half-finished projects and orphan needles missing their partners. And she’s always dropping stitches and accidentally adding them, so her projects are all wobbly and lumpy and full of holes.
Cassandra knits; most of the military folks at least know how to make their own socks. That doesn’t mean she’s any good at it. After one look at her coarse, gray, lumpy socks, Cassandra receives a a bright striped pair from Dorian and a perfectly crafted pair from Vivienne.
Cullen knits for the same reason, though he’s a bit better at it. He takes up knitting in earnest to cope with the lyrium withdrawal, and soon his room is littered with socks (it’s the only thing he knows how to make). They’re perfectly good socks, but very practical and plain, and Dorian keeps trying to get him to use more colors. Or to learn to make something different, but Dorian can’t knit and Cullen is hopeless at crochet, so there’s only so much he can do.
Leliana has totally crocheted tiny sweaters for her pet nugs.
The Iron Bull gets yarn bombed by Dorian, and Dorian is utterly taken aback when Bull retaliates in kind a few days later, mostly because “What kind of stitch is that?” And that’s how Bull shows Dorian Qunari crochet (i.e. the Thedas equivalent of Tunisian crochet).
Cole cannot knit, or crochet, or anything. The others try to teach him, but he always tangles the yarn and seems perfectly content to sit around unknotting it.
Varric’s a city dwarf, and hasn’t ever really been in a situation where couldn’t just buy new socks when he needed to. Hence he does not know how to knit or crochet, which makes him the perfect person for all the others give all their random projects to.
Blackwall crochets, though he’s a little rusty at it. He goes to Dorian for advice for something nice to make for Josephine (or the Inquisitor). He doesn’t say outright of course, but Dorian recognizes the little crocheted flower tucked into Josephine’s clipboard.
Josephine never learned how to knit or crochet herself (she’s a noble lady who was supposed to learn embroidery, though she’s not much good at that either). She is very much in awe of people who can do crafty things like that. Eventually she learns how to crochet (probably from Blackwall or Dorian) and makes little plushie dolls of her friends.
Morrigan knitting tiny baby outfits and blankets when Kieran is born, and infusing them with protective magics. Morrigan making hats and scarves for Kieran when it’s decided that they’ll be heading into the Frostbacks. Kieran picking out the colors because Morrigan still has no fashion sense. Morrigan teaching Kieran to knit to help calm him down from nightmares. Dorian teaching Kieran to crochet, because Kieran’s the sort who likes learning new things. Kieran making crocheted gloves and scarves for Morrigan and Morrigan wearing them proudly.