Being here suburbs of Helsinki, my only worry in the very cold we had over the weekend was if car started (it did!)... I only play tennis in the winter nowadays (no time in the summer really, and getting adjusted takes time...)... but we have great indoor courts. No problem playing in -25C when it's 20C inside on the court.
The outdoor courts, well, they are closed, they take the nets off etc. So basically there's the May-Aug outdoor season and then the rest of the year indoors. As a kid, I only did the summer season (played daily), now clay courts don't really call me anymore...