I see TWO statements here:
#1). Earth is much farther away from the Sun in Winter.
#2). That's what makes it cold in the Winter.
Let's use our heads on #1 for just a little moment:
-- When it's Winter in Canada, the USA, and France, it's Summer in Australia, Paraguay, and Namibia. This is the end of December, all of January and February, and most of March.
-- When it's Winter in Tasmania, South Africa, and Botswana, it's Summer in Germany, Israel, and Mexico. This is the end of June, all of July and August, and most of September.
So WHOSE Winter is the question asking about ? ? It doesn't say.
Earth is FARTHEST away from the Sun during the first week in July, and it's NEAREST to the Sun during the first week in January.
The difference between the nearest distance and the farthest distance is about 3%. It has almost ZERO effect on how hot or cold the days are. Anywhere !
So BOTH of the statements in the question are FALSE.