Using the word 'come' to mean 'when it comes'
This usage is not mentioned (at least as prepositional) in many of the online dictionaries. However, Google Dictionary includes it:
come preposition [informal]
- when a specified time is reached or event happens. "I don't think that they'll be far away from honors come the new season"
It almost certainly derives from the common verb, with deletion (perhaps of 'when') and re-ordering. As this dictionary says, it wouldn't be used in a very formal register, though I wouldn't restrict it to informal ones. It does have a 'chatty' feel about it to my British ears.
Well, it is not particularly common but yes, it is correct. Specifically, this is the meaning 2c(2) from the online Merriam-Webster:
c (2) : take place —used in the subjunctive with inverted subject and verb to express the particular time or occasion <come spring the days will be longer>
It is not often used in day-to-day speech but you can still find it as you saw.