It really depends.

How skilled are the bowmen and how strong are the bows?

Despite what you may think the force of the arrows impact is generated on the downslope. Up close firing at a target is fine and could put someone down. I'm assuming you're talking about a shower of arrows from a distance.

So if you have a bunch of guys with short bows the force of the string is pretty low. This means the arc has to be pretty shallow and therefore there isn't much force generated. Shields could easily stop them. I imagine it was still terrifying.

Take the welsh long bows. Huge bows able to hold much heavier arrows and launch them very high and very far. These arrows had much more punch and could easily puncture wood or chain mail. A frightening prospect considering most people on the battlefield didn't wear chainmail.

Either way frightening. A long bow because of gravity and it's ability to launch a heavier projectile in defiance of gravity makes it an amazingly deadly weapon.