And the wolf is a mount, so you can't use other mounts except the wolf transformation, and speed boost items are useless, as like I said the wolf transformation is a mount and your speed doesn't exactly increase via items, but your speed can still decrease however by debuffs.
Also you cannot double jump as a wolf, and the only item which you can rely on using for fall negation is the Lucky Horseshoe and yet again can't use Grav Potions or Rope to get to floating islands that simply.
Playing as just a wolf has its downsides but has some advantages due to high jump and fast speed.