The overwhelming majority of homeless people in California lived in the same county they currently do before they became homeless. Climate is clearly not the main factor.
71% in SF homeless already lived in SF, 90% already lived in California: https://socketsite.com/archives/2016/02/san-franciscos-homel...
the cite link in that article is dead but refers to http://hsh.sfgov.org/wp-content/uploads/2016/06/2015-San-Fra...
75% of LA homeless already lived in LA: https://www.lahsa.org/documents?id=2059-2018-greater-los-ang...