I am always quick to give money and food and smiles to the homeless and I have in the past brought some home. At the time, however, we lived in a house where we had accommodation separate to the main bedrooms so it was quite easy and safe. And then there's the times in another house where I did let the occasional homeless teenager move in for a while, but my kids knew them from school so they weren't exactly strangers.
You are faced with the same moral dilemma that occasionally prevents me from executing a generous gesture. We really must not sacrifice our own children's safety and welfare in trying to help others. Your children have to be able to sleep safely in their beds at night and it is impossible to tell at first glance just how trustworthy any individual really is.
I appreciate that I might get robbed and that would be no fun but I'd get over it. What I wouldn't get over is if one of my kids was to fall victim to a stranger in my home.
If I was you, I'd keep an eye out for little one or two-person tents in discount stores, buy a few of them and keep them in the back of my car. I'd also be watching for warm woollen blankets in charity stores that can be purchased cheaply.
Occasionally you could hand out a tent and a blanket for a homeless person's longterm use - and still sleep soundly in your own bed at night. :)