Eh, I'm tempted to say just deal with a dirty car for a week or two until it warms up. This is Philly - cold spells don't typically last more than a week or two. You can wash the car on your own once it gets above 40*F.
2011 BMW E92 335i, 6MT, Le Mans blue - Quaife LSD, JRZ RS Pro, JRZ camber plates, Eibach ERS, full M3 susp, custom toe arms, Powergrid end-links, SS brake lines, brake ducting, Michelin PSS, UUC SSK, ETS FMIC, ER CP, Perf. Exhaust, VAC RSIK, Sparcos; work by VAC Motorsports in Philadelphia