I agree with you. In English, you don't have to use THE with winter. Both are correct.
The meaning is the same. The only question is, whether it is acceptable as a translation.
It would be "A tél hideg." You need the definite article in front of the noun in these general statements.
But not for some proper nouns. Or none? That needs to be figured out.
Péter is tall - Péter magas
Hungary is beautiful. - Magyarország gyönyörű.
Winter is cold - A tél hideg
Cars are fast - Az autó gyors
Apples are healthy - Az alma egészséges
Yes, the general statement even changes to singular, most of the time.