Car Engine Light On, shaking and jerking. Extreme cold in the region

It has been very cold here all week, not reaching more than 10 F. Today I went to start my car and the engine light came on. The car was also shaking while I was waiting for it to heat up. Once on the road it kept jerking and shaking especially after trying to reach a speed of 40miles and hour. It kept up the whole ride which was about 35-40min. Car has only 19336 miles on it.