Ship the M3, peace of mind. Jan/Feb is considered the coldest month in Chicago, it extremely cold, sub zero temp, wind chills lake effects go below Negative from 1-10+.
Last time I drove my M3 was back in Aug 21. since then put it in hibernation hooked up a C-tek trickle charger. plan on taking it out and put some heat in the motor during spring/fall timeframe when my current job schedule allow me to.
I had Pilot Sport AS3 on my beater Honda, work perfectly fine, they salted and plowed the St/Highway very consistent.
Good Luck on your Move and Welcome to the windy city. get yourself a Bullet Proof Vest. JK....