The Jack Reacher Method
one reason for those stolen carts is to carry around heavy bedding in winter...People with shopping carts full of crap inevitably have TERRIBLE hygiene in part because you can't keep your giant pile of crap CLEAN while homeless. A lot of homeless people have health issues and this is a recipe for staying sick and getting sicker -- or becoming unwell if you weren't sick to begin with.
I once talked on Reddit about how, while homeless, I would get a change of clothes and throw the old ones out and someone called it The Jack Reacher Method. Here is a clip of Jack Reacher going to a second-hand shop and changing clothes.
I did that for cleanliness reasons and logistical practicality. I didn't feel it made sense to try to hang onto dirty clothes long enough to come up with enough to justify a trip to a laundromat and if you get super cheap clothes, a change of clothes can be less expensive than paying for cleaning them.
If you are in homeless services, I wish someone would allow homeless people to get a shower and free change of clothes and turn in the old clothes for laundering rather than people like me throwing them in the trash.
Keep it to stuff like t-shirts, sweat shirts and sweat pants. There are too many services trying to dress you for a job interview and too few trying to dress you for surviving on the street.
I did my best to carry one bag. I was homeless with my sons, so we reached carried a bad and split up our supplies but I would try to stick to one bag even if I were alone.
We managed winters by having three people in a small tent with two or three blankets. If you're alone, it probably makes more sense to have some kind of bedroll or sleeping bag. I thought about it and concluded I would probably get a silk sleeping sack if I were alone because they are extremely lightweight and compact and would help me keep it down to one bag.
I wish homeless services would also supply lightweight sleeping bags of some sort that helped homeless people keep it down to one bag and allow you to periodically trade in the old stuff for another set, launder it and give it out again.
I think staying healthy or getting healthy is the single best thing a homeless person can do and traveling light and just ditching your old clothes and blankets is the most effective way to do that while being able to get into grocery stores, libraries, eateries, etc.
You may wish to also read my old archived blog the San Diego Homeless Survival Guide written while I was homeless. And posts on this site tagged Homelessness.
I made small amounts of money online, spent my days in libraries to keep my laptop or phone charged and use their Wi-Fi and found services that gave me free or cheap clothes and food essentials. I did everything I could to arrange a mobile lifestyle with some hope of rebuilding my life and staying healthy and getting healthier while building a portable income was my top priority.
People dragging around a giant pile of crap strike me as hindering their quality of life today and not in any way improving their odds of getting back into housing. I'm not trying to "judge" those people. I'm hoping to offer better answers.