I am the owner of Hyundai Accent with a diesel engine. After very cold nights, the mornings are a nightmare. The engine starts fine but a light for check up is on most of time on board, and after gear 3 the engine dies. This is happening ONLY after a very cold night; when temperature is +1 and over everything is ok...any suggestions?
Your glow plugs may be bad. "Check Engine" light may also mean faulty glow plug (checked that on 2009 SEAT Ibiza with Ross Tech VAG COM).
Faulty glow plugs may be the case, but you can tell that from the way your engine works. If upon start your engine is shaking (not working very stable) or your revs are a bit jumpy, then it may indicate that fuel in some cylinders are not burned.
If this really is the cause, then after starting the engine try leaving it idle for few minutes. Glow plugs are needed only to heat up cylinders on start, after some time they get hot from all explosions and diesel does not need them anymore (diesel explodes from compression and high temperatures).
Faulty glow plug may also produce smoke (white smoke / unburned fuel) but in cold weather it is hard to know since there will be much more steam coming too.