She needs a routine. My kids had them from the start - whether it was daycare/preschool/home/school - jackets/hats/hoodies/belongings went in cubbies or on hooks.
Keep it the same wherever she goes. Some kids need more structure/routine than others. Kids who are a bit 'scatterbrained' (or who just get to a place, see kids or toys, or activity - and go!) need routine even more.
There are kids who go through life like this and become adults who misplace stuff - keys, etc. It's just their personalities. Those are the people who need those places right by the door for their keys, etc.
We always had a cubby by the door for each of our kids when they were little (that age) and everything went there at end of day. Otherwise, we never would have found their stuff. It mimicked what it was like elsewhere. Even if it's unorganized at summer camp (and you can't always expect counselors or teachers to keep an eye out for everyone's gear), just get her to put it in one spot every single day or her bag. Who is picking her up? If it's dad, tell dad - GET her jacket before you go. Have a post it note in the car by dash to remind him (or a reminder on his phone) whatever works.
At 6, not all kiddos remember this. I always reminded mine when picking up from sports, activities, etc. "Do you have water bottle?" etc.
If she doesn't have a backpack, maybe pack her one, and everything she takes off, goes inside. That way, all together and doesn't get mixed up with everyone's else's stuff. Easy for her to grab at end of day.
Good luck :)
ETA - just wanted to add, at that age mine brought home other kids' snowpants from school (one time, my kid wore two pairs home, one pair on top of the other..), hats, mitts have been lost, lost water bottles .. etc. It's kind of the norm, so know that even with routines this happens to most kids and families.