Avoid camping near other people if you want to avoid anything of yours getting stolen. Anything that you can't carry with you, at any time left unattended is at risk of being stolen, so keep that in mind. You're definitely going to want clothing and a sleeping bag suitable for the cold temperatures, and probably a portable propane heater or stove. If you need to keep a phone charged, a small portable solar panel with a USB port will be valuable. If you can't afford those things, it will be a lot harder.
Normally, I'd advise finding an abandoned building to camp out in, but I'm not familiar with the Denver area or what is available there, so while doing such worked for my unique set of circumstances, that may or may not be bad advice for your set of circumstances. When I was homeless, it was in a warm climate in South Texas.
Always make sure you can pack all your things up in minutes and relocate. Anywhere you camp can attract other homeless people, who may steal from you, or could attract law enforcement who might harass and/or arrest you. Anyone that sees you enter your camp location is a potential snitch, thief, or worse.
Having spare sets of socks goes a long way toward not feeling filthy, in the event that you don't get to bathe often. Wet wipes are good for cleaning yourself if you can't access shower facilities. Carry at least 3 sets of clothes. One to wear, one to change into after you get cleaned up if given the chance, one as emergency backup.
A bicycle kept in usable condition will go a very long way toward helping you carry out day to day tasks and to help carry your stuff efficiently. I'd highly recommend one for transportation so you can avoid having to pay for the bus.