2008 Chrysler 300 help

The place to start is by reading and recording the diagnostic fault codes. Chrysler makes doing that yourself much easier than any other manufacturer. Cycle the ignition switch from "off" to "run" three times within five seconds without cranking the engine. Leave it in "run", then watch the codes show up in the odometer display.

When you have an engine-related problem, please list the engine size.

First I would suggest that you get the codes read and cleared then post them here for us.I would suspect a code c121c, which indicates a an abs/traction control system issue. It is very possible that you may have some broken wires or unplugged or broken sensors from going thru such deep snow. Or possibily some moisture into one of the modules. Please let us know what the codes are and if the symptoms change any after the clearing of the codes.