Urban Arrow sells a custom rain cover that attaches directly to the cargo box frame. Zips closed at the front, has a clear window panel so kids can see out. Kids stay completely dry in heavy rain. Keep a spare in the box — NYC rain is unpredictable. The cover also blocks wind entirely, making it the most useful cold-weather accessory for a front-loader.
Longtail passengers sit in the open, so kids need rain gear: a proper rain suit (waterproof jacket and pants) and waterproof shoes. A handlebar-mounted canopy adds overhead protection and extends the range of conditions you can ride in comfortably.
Wind chill is the bigger factor than ambient temperature. On a front-loader with the cover closed, kids are sheltered from wind entirely and stay surprisingly warm — many families find their kids overheat on mild winter days. For open longtail riding: fleece underlayer, wind-blocking outer layer, gloves, and a thin hat under the helmet. Bunting bags like the Snuggler wrap the child's lower body and are very effective for toddlers.
NYC rarely drops below 20°F. Most of winter sits in the 25–45°F range. With the right setup, the vast majority of winter days are rideable. Snow and ice require more care — studded tires make a significant difference on icy roads.