V.P.
Both my kids have had and have attended swim parties with snow on the ground. Indoor pools are warm and fun and well supervised. And yes, I don't see the problem with inviting boys, even as a tween. My daughter doesn't have any close friends who are boys, but my son has friends who are girls. It would be wrong to exclude them just because of their gender. I think it's unfair to exclude close friends on the chance they might have romantic feelings. It does happen at this age, but it also happens they can just be innocent friends.
And in terms of 12 or 2:30, it's really about whether you want to serve lunch or not. If it was 12, I'd serve pizza in addition to snacks and cake. At 2:30, I wouldn't.
ETA: Invite the whole class? I can't imagine inviting the whole class at this age. I would pick 6 to 10 of her closest friends and be done. Don't pass out invites at school, though - that's rude if you're only inviting some.