There are a variety of reasons.

First of all, cold is better than warm. Very few major cities in the U.S. really get life-threateningly cold - Minneapolis is about the only one that comes to mind immediately - and it's a lot easier to get warm than it is to get cool. Having to wear a few more layers and use a few more blankets during the winter is a lot better than being constantly bathed in sweat during the summer. Remember, if you're living on the street, you probably only have intermittent use of showers - and sweat stench is a huge impediment even for those living on the street.

Colder climes also tend to have better services. Your average social services person has the same basic attitude you do - heat is no big deal but cold kills people. As a result, homeless shelters and other such accommodations start dropping off rapidly the further South you go. People say "oh... it's 70 degrees out, the homeless can just sleep on a park bench". However, the lack of beds also translates into a lack of soup kitchens, mail drops, storage lockers, showers and other services that the homeless use.

And, of course, there's the simple reality that most of the homeless you see in the cities lack the ability to actually go anywhere. They don't have the skills to live off the land or travel long distances on foot, they don't give off the right kind of vibe to be successful hitchhiking, they don't understand how train yards work, etc.

Lastly, 'homeless' is generally less a state of being than a temporary inconvenience. The bulk of the homeless you see are merely in one stage of a cycle that includes crashing on people's couches and moving through various parts of the social system. They're not planning to move South for the winter since everyone and everything they know is here and they don't plan that far ahead (or expect to still be homeless).