Good point. I don't think of Catholicism when I hear the word "veil".
Nuns that I know do not use this term. Though I admit that I only know one young nun, most that I know are older. Possibly it's a trend among these younger women entering the religious life.
Last year I met a fairly young Dominican (from Nashville). She used the word "habit". She also mentione that the sisters in her order also enjoyed a good round of rugby. I kid you not. I asked her to please send me a photo of the "scrumming nuns", but I think she forgot.
I know that Conan Doyle's historical novels use the term, and I know I've heard it used more recently (like in the 60s, before all this divesting of habits started.)
"Taking the Veil" is an old phrase, very traditional.