There are local clubs which swim from the island on a regular basis, year 'round. If not absolutely daily, several times a week.

Water temps vary by time of year, but are particularly mild from late summer through late fall. Even winter-time temps aren't particularly challenging. A dog could easily make the swim.

Currents are a challenge, but mostly if you're planning on landing at a specific point along the shore. If your goal is simply to make it to shore, they're far less an issue. Just swim cross-channel and you'll make it.

The physiological and psychological challenges are greatly overblown.