Yes, फ़रवरी का महीना छोटा है is also correct. Hota hai” / “Hote hain" -a conditional case is often used when talking about the inherent qualities of the subject. In this example, "shortness" is a quality of February since it is the shortest month of the year; "Coldness" an innate quality of "ice" and so on. However, in DL lessons and in the common parlance, it appears this usage does not always follow the rule.
It's hard to explain, but usually nouns in English need an article (a/an/the), a possesssive [my, her, theirs) or demonstrative pronoun (this, that, such etc). Here it's month that needs 'the' - you have to say 'The month of February'. February itself is a proper noun, a name, like Rupesh, Monday, India etc, and doesn't need an article. The reason 'man' in your example doesn't need an article etc is because it's a collective noun, meaning all of mankind.