This would be common vernacular around where I live. In fact, it would be much-preferred over the correct but a bit estranged, ""February is not a month of summer."
My own translation is also okay, "February isn't a summer month."
But honestly I prefer yours. Is this added yet?
You must negate your sentence. The Spanish sentence demands the translation be, "February is //not// a month of summer." I prefer your form to the other, "February is not a month of the summer," but I will also say that this is a less-preferred English phrasing overall.
To help you better attune to the English mind, a native would commonly prefer, "February in not a month //in// summer," or the format that used the word "summer" as an adjective, "February is not a summer month." If you're in trouble, however, your translation would be perfectly acceptable to the English ear in common conversation and probably wouldn't raise eyebrows.