If you look at shields from graves, you frequently find traces of leather beneath the boss or under the rivets, indicating that the face (and often the back) of the shield had some sort of leather covering. I'm most familiar with Anglo-Saxon shields, which almost universally have leather on one or both sides. To my knowledge, it's equally common for Viking Age shields (the main exception being the Gokstadd ship burial, though those shields were very likely made for show during the burial rather than use, so interpret with care).

But was that leather tanned or rawhide? It's incredibly difficult to answer archaeologically, because all that survives is usually whatever fibers are corroded into the rust. Those fibers tell us there was leather on the face of the shield, but not how (or whether) it was tanned because there's not much there to chemically analyze.

So to answer the question, you have to use a bit of experimental archaeology. Leather can improve the strength of reproduction shields, but rawhide works much better (it's much harder). When waxed, rawhide can be reasonably water resistant. And, perhaps most importantly, it's a lot less labor intensive to make than vegetable tanned leather. None of this proves that the leather we find on shield faces was rawhide rather than tanned, but it suggests that that would be the better guess.