Yes, covering all the statues for all of Lent was a practice when I was much younger. But I don’t think there is provision for that today.
Paschale Solemnitatis says:
It doesn’t appear from that that statues and crosses should be covered this year until April 5th.
That’s just the crucifixes, which should not be covered UNTIL the 5th Sunday.
Covering the statues, however, is entirely optional either way.
There is no requirement that statues be visible in any Church at any time (I think it’s a good thing, sure, but there’s no requirement to have them), so covering them is just a matter of preference.
In fact, the instruction from P.S. says that lights should not be lit in front of images of saints after the Mass of the Lord’s Supper. When I read that, it seems that it’s leaving open the possibility that the statues are not covered at all.
I think the whole covering or not covering statues during Lent is more of a cultural thing.
See Paschale Solemnitatis #29. It leaves the matter open, rather than universal, although if they are covered, they aren’t uncovered again until the Vigil.