…………. to see what it's like to sleep without formal shelter or security.
………… I would take my dog with me, my sleeping bag and an extra blanket if it is insufficient, a flashlight, a watch and toilet paper. In the interests of not attracting bears I would not take any food, but maybe a thermos of hot coffee. ………………………… ………………………… I would not have to 'camp' alone ………
Even smarter would be if I made a visit to the local police outpost to let them know what and why I'm doing. …………
With that much preparation, will you really be experiencing what it is to be homeless? I don't suggest that you put yourself as risk, but surely the lack of security is a central consideration. Whether you have a good night's sleep or the worst night's sleep in your life, I suggest that you will be doing it safe in the knowledge that you'll be snug back in your bed the following night. What you won't experience is the desperation that this could be as good as it gets.
As the suggestion has come from homeless people themselves, it might give you some street-cred in interacting with them in the future but there may be others who see your gesture as little more than tokenism.