Why are so many people resistant to seeking or receiving help from shelters and outreach programs?
Because in a shelter they are apt to have there stuff stolen, be assaulted, sexual molested etc. etc.
I like edgars idea of supplying them with some emergency rations, and warm clothing, particularly socks, gloves, thermal underwear and hats. If you can keep your extemities warm, you're in better shape. Especially keeping feet warm and dry.
The city can purchase those items wholesale. At a quick glance, the socks, gloves and hats could be procured at around a dollar each.
A set, top and bottom of thermal underwear can be got for around $6.
So for let's say $10 you've fortified someone for cold weather.
Add in emergency mylar blankets that are waterproof, check the wind and hold in heat, for another dollar each.
There are those hand warmers that give about 10 hours worth of 130F heat. Put them in your shoes, or gloves, or on your chest, etc. They are cheap too.
Compare this to the cost of however many people end up in the hospital, and/or forcing them into shelters.