Because Harry had to retrieve the sword in dangerous circumstances.
In Snape’s memory at the end of the book, we see Dumbledore explain to Snape that Harry has to retrieve the sword in an act of bravery:
“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 —”
— Deathly Hallows, chapter 33 (The Prince’s Tale)
What would happen if the sword was left in an easy place for him isn't well defined, but perhaps the sword would retreat to the Sorting Hat if retrieved in such an easy way. It's probably not particularly amenable to being passed around freely.
(The rules defining “worthiness” to use the sword seem quite fuzzily defined, but it's the best we have.)
Indeed, Harry guesses as much when he's about to dive into the lake:
What was it, Harry asked himself (walking again), that Dumbledore had told him the last time he had retrieved the sword? Only a true Gryffindor could have pulled that out of the hat. And what were the qualities that defined a Gryffindor? A small voice inside Harry’s head answered him: Their daring, nerve, and chivalry set Gryffindors apart.
Harry stopped walking and let out a long sigh, his smoky breath dispersing rapidly upon the frozen air. He knew what he had to do. If he was honest with himself, he had thought it might come to this from the moment he had spotted the sword through the ice.
— Deathly Hallows, chapter 19 (The Silver Doe)
It's not daring to pick up a sword that's been left lying around.
Snape's memory finishes when he leaves Dumbledore's office to deliver the sword. I assume that he was watching Harry to make sure it was retrieved safely, and would have saved him from drowning if Ron hadn't intervened (but perhaps confunding him afterward so Harry didn't remember).
As for why he picked an icy lake? Snape has to keep Harry alive, but he also hates him and will happily see him suffer.