From my work experience (I deal with homeless on a regular basis) and know a few people that work in shelters, I've learned a few things over the years.
Homeless shelters aren't pleasant places. A lot of them are infested with bedbugs and other things like scabies etc. A lot of these people are extremely sick and disease spreads easily. Sure some of them will go there to eat, but rather would brave the cold instead of sleeping there over night. In a lot of these places they will get robbed by others, including some of the shelter staff.
One homeless guy I have consistently ran into for the past few years says a shelter is the last place you will find him....this coming from someone with nothing was kind of shocking at first, until I learned more about these places. My friends that work at the shelters confirmed all of this stuff I've heard. It was a real eye opener.
Just my $.02