Are Hogwarts students allowed to swim in the black lake?

I don't think there's an actual rule about it, because in Snape's memory from OotP, Lily and her friends are dangling their legs in the water. The Weasley twins and Lee Jordan are always feeding the squid.
And besides, if they weren't allowed to swim in the lake, they wouldn't have had the lake task in Goblet of Fire.

i dont belive so beacuse theirs a giant squid but i could be wrong

I don't think they are. No one is ever mentioned swimming except for in the Triwizard Tournament.

They're has been no part in the filmes where they go swimming in the lake except during the Tournament in The Goblet of Fire.

I don't really think they are.

I'm pretty sure that in book 4 Viktor Krum was swimming in it, because I remember Hermione saying something about how it might be cold for them, but it was colder where Viktor was from. Hope this helps :)

I think their allowed, but no one dares to cause of the giant squid, and because except for about 2 months, it always to cold to swim

I don't think so. Too much merpeople and there's also the squid.

I think they are, and there are no rules going against it. But it's highly unsafe to go in full on knowing there is the Giant Squid, merpeople, and who knows what else.