Don't fret!

They will go away.
Not by resting, or waiting, or fast traveling.

You just have to go find yourself another enemy archer, and all the arrows will dissipate after you've gotten shot again.

But then you got new arrows in you and the circle starts all over again!

Nah, they disappear once you've gotten shot again, promise.

You just want target practice, you n'wah!

This happened to me once, the persistent arrows thing. I tried everything, then thought of being shot by another arrow. But I figured that by then I had already played about hour since the incident, and finding another archer to shoot me would probably take longer, and the arrow through my character's head was bothering me so much, and since I wasn't sure I was ever going to fix the arrow, I decided to sacrifice the time I had already played, reload and not get shot by that goddamned archer.

I turned into a werewolf and they dissapeared, but now im clean again, so thnx for this advice

Yeah, going beast fixes it too.

I just dropped the arrow from my characters inventory... but this should also work on 'em ice projectiles!

A faster solution for PC users is to go into the console and type sixchange twice.

Going Werewolf form clears all arrows and spell particles from you.

I got rid of mine by removing the aroows into a container, then putting them back into my pack.
I have about a half dozen arrow types in invewntory.
I shoot whatever I has the most of at the time.

Equipping arrows would clear them in Oblivion.

I avoid using the console on the PC, last I checked doing so disables achievements during that session of play.