Yes, I have swam there. No problem!

I don't remember seeing any signs against it, but it didn't look very inviting.

Yes. When I was stayed there were at least two docks where people were launching small boats and jumping in to swim. I suppose if you were up for it, you could wade in from anywhere on the muddy, shallow, grassy shoreline.

None of the signage prohibits it. Call 307-473-3400 if you're concerned.