As winter quickly approaches, Gov. J.B. Pritzker on Thursday announced plans for the state to spend an additional $160 million to aid and house a sustained influx of migrants sent to Chicago from the nation’s southern border.The administration sold the plan as a three-phase approach: “welcome, shelter, independence” — aimed at meeting the needs of migrants based on how long they’ve been in Chicago and whether they’re planning to stay.The state will spend $65 million to create a winterized “soft shelter site” to address …