Car is shaking when I start it and check engine light is on!

I drove my car yesterday and everything was fine. We had our first snow last night (not sure if that has anything to do with it) and when I went to start it up, the car was shaking uncontrollably and the check engine light came on(solid, not flashing). Is there any way to figure out what it possibly could be without getting it scanned from a mechanic (I'm a college student and do not have the money for an expensive fix =(.) Also, IF I do have to drive it somewhere, is it safe to drive while it's shaking like that? Thank you!