It shows nothing of the kind. Perhaps, if you were living somewhere with a lethal climate, and you became homeless, you would leave.
Or perhaps you would stay, thinking "homeless presence has nothing to do with the weather", and die. In either of those cases, the weather has shrunk the homeless population.
71% of homeless people were living in SF just before becoming homeless. Only 10% come from outside of California (and its climate)[0]
This pretty clearly shows homeless has alot more to do with the cost of housing relative to wages jobs then good weather.
[0]pg 33 of http://sfgov.org/lhcb/sites/default/files/2015%20San%20Franc...