Snapedom

I think we all agree that no one would put the sword in a pool of icy water unless
(a) they were a jerk or an idiot or
(b) it was actually necessary.

You mention that portraits can only know what happened up until they were formed (unless told); the portrait was created by Hogwarts after Dumbledore's death (implied in the text and also interview canon), thus it knew everything Dumbledore knew at his death, including what had happened in Harry's first year and what Dumbledore had written in his own will.

From p. 689 of my American hardcover DH:

Phineas Nigellus came hurrying into his portrait.

"Headmaster! They are camping in the Forest of Dean! The Mudblood --"

"Do not use that word!"

"-- the Granger girl, then, mentioned the place as she opened her bag and I heard her!"

"Good. Very good!" cried the portrait of Dumbledore behind the headmaster's chair. "Now, Severus, the sword! Do not forget that it must be taken under conditions of need and valor -- and he must not know that you give it! If Voldemort should read Harry's mind and see you acting for him --"

So. Either
(a) Dumbledore said that for no reason *and* Snape is a jerk or an idiot, or
(b) the sword has to be taken under conditions of need and valor each and every time, and Dumbledore and Snape acted accordingly.

I'm gonna go with (b).