Forcing homeless people into shelter

Rich Coleman is musing about finding a way to force homeless people into shelters when the weather makes life on the street dangerous. The media interest was raised after a woman who had declined shelter burned to death in her shopping cart while trying to stay warm.
It's an issue worth considering, but as Coleman notes, there are big legal and ethical issues and nothing will happen soon.
Rather than mess about with complicated legal questions, Coleman could address the issue now. The woman who died chose to stay on the street in part because going to a shelter would have meant abandoning her shopping cart and all her worldly possessions. It would not be hard or costly to have secure outdoor space for carts at shelters, staffed by a minimum wage worker making the transition from the streets. Other homeless people chose a doorway because available shelters won't take their pet or allow couples to stay together, or because the available spaces are just too chaotic, noisy and theft-prone.
Making improvements to address those problems would be fairly cheap and easy.
Also, Coleman talks about forcing people into "beds," when in many cases the reality is a mat on a floor in a large room. That's better than nothing, but more accuracy in language would help in dealing with a complex issue.