I understand that when beavers walk on land, they drag their tails behind them on the ground. Their tails look quite large and rather heavy, and the ground is often rough - does dragging the tail not cause abrasions and pain for the beaver?
No, it does not, otherwise beavers wouldn't walk with their tails dragging. Here is a picture of the bottom of a beaver's tail:
and here is a closeup (probably of the top, but they're very similar):
Royalty-free stock photo from Dreamstime
As you can see, the skin looks almost like reptilian scales. It is likely highly-keratinized and is quite thick, as you can see below. Innervation is probably net very close to the surface, like callouses we develop on our hands and feet, so it doesn't hurt to be dragged over sharp surfaces like rocks or thorns. Here is a cross-section of the thick part of the tail close to the body:
Source: Cannundrum blog