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 335i E92 - Le Mans Blue, 6MT, M Sport. JRZ RS Pro, Quaife LSD, BMW Perf Exhaust