While this may be something that has happened, this definitely is not something "the homeless do" in the US

Ive only ever heard this as a random anecdote with no real evidence. Not saying it doesn't happen, but I'd guess the percentage of people who do is probably miniscule.

the homeless

do you mean "homeless people"?

often known to commit minor crimes

do you mean "are rumored to"?

before a cold front, so they can stay in jail where it's a bit warmer

do you mean "so they don't actually freeze to death on the streets"?