Dear Colleagues,
I have a question concerning the following sentences:
It happened in a cold winter night.
It happened at a cold winter night.
 
Which one is correct? 
 
Someone even suggested a 3rd solution: "on a cold winter night"
 
I now that we say "in winter" and "at night" but what about "winter night".
 
I guess that the first sentence is the correct one, because the word "winter" is closer to the preposition.  Am I right? 
 
Thanks for your help in advance.
 
Adryenn