Technically it's not a horn but a tooth that grows upwards through the skull.

However I'm not sure what the unicorn horn is made of.

Swimming in the ocean, causing a commotion because they are so awesome

Warm in these narwhals.

But narwals eat fish and unicorns eat flowers.

Maybe there are real narwals and fake unicorn narwals. The unicorn ones only show up in the summer for their breeding season.

That's unicorn propaganda to mislead the masses.

Like Vampires not having reflections or British people having manners.

However I'm not sure what the unicorn horn is made of.

Keratin.

Remember, The Narwhal bacons at midnight.

How does one bacon?

Indeed -- assuming they're related to horses, they're not artiodactyls like goats and cows with keratin-coated bone horns, and it wouldn't be a dentin tusk like narwhals and elephants; they're perissodactyls like rhinos so they'd presumably have keratinous horns that grow back, like hooves and turtle beaks.

No, you misunderstand. I wasn't speculating; I just looked up the Wikpedia page on them and the info was right there.

With gusto

They'd beat a polar bear in a fight!