Covered with snow,

Covered with snow, John could not enter his car.

Covered with snow, John could not enter his car --- John is not covered with snow which this sentence suggests, so incorrect.
Covered with snow, John's car could not enter ----- illogical and makes no sense.
Covered with snow, John could not get into his car ---- same as the first sentence.
Covered with snow, John's car could not be entered ----- wordy
John could not enter his car because it is covered with snow---- this is correct.

Many times, omitting the modifier and including a conjunction does make the sentence sound better!

because of same reason, i marked E but OA:D
Later i thought that E uses wrong tense and that might be the reason - could and is should be both present or past... what do you think

Oh i totally missed the "is" in the sentence.

Yes, you are right, in that case, E is not correct and the correct answer choice is D.