Are you implying that the presence of any homeless people in New England invalidates the idea that consistently favorable weather leads to a higher ratio of homeless people living in an area?
Probably also matters long term vs short term. When someone first becomes homeless, it usually happens where they were already living regardless of the weather. Over time, people may move to where it is more comfortable to sleep outside.
So, all cities have new homeless people plus some that just never leave. And then warm areas have new homeless people plus the long term homeless people who risked traveling to get to warmer temperatures.