"Today is February second."
Pretty much only the US uses that format. Japan actually uses year month day format. To make it more confusing they use 2 different systems day to day. There's the Gregorian calendar then there's the imperial calendar. They starting from the year the Emperor was crowned. As an example, in the 10th year of the Showa emperor would be Showa 10.
二 日 would have be together as it would be "two days" when seperated. When it appears as 二日 it is classified 2nd.
As the sentence said "February 2nd" the sentence was actually "Today is February Two Days."
But you can use it in sentences like: 彼女は_に二日かかりました。(She took two days to ___.) or 二日間雨が降っています。(It's been raining for two days)