Winter month is a normal way to say it in English. Names of seasons can be used like adjectives in front of a noun, like "winter month", "summer olympics", "Nothing feels as nice as a spring breeze", or "On a cold autumn morning, frost lay on the ground." Names of months, and days of the week, can be used the same way.
"February is a month of winter" makes perfect sense but sounds a little more dramatic, or poetic, than "February is a winter month."
The -i suffix is a little hard to explain. It turns a noun into an adjective, but in the English translation you wouldn't usually make a difference. It is mainly used to form compound nouns, like "winter month". You may also think "winterly month" if you like.
An example where the -i does make a difference in English:
ipar - industry; ipari - industrial