are they natrual?
1.In winter or in the winter in 2013, they started their new business.
2.I ran into my old friend Tom in the street in a day of winter or the winter in 2013.

Thank you!

Question

are they natrual?
1.In winter or in the winter in 2013, they started their new business.
2.I ran into my old friend Tom in the street in a day of winter or the winter in 2013.

Thank you!

Answer

Here are some suggestions:

1.In the winter of 2013, they started their new business.
2.I ran into my old friend Tom in the street one day in the winter of 2013.
  I ran into my old friend Tom in the street on a winter's day in 2013.

Answer

Simply the use of the article THE is for the known things and already identified names, or objects ...etc.
Anything that has been introduced for the first time in the paragraph, must be unknown so no use of the article here.

So, to rewrite your statement although I am not so sure what do you want to say but here we go:

I ran into my old friend Tom in the street in a cold day in the winter of 2013.