Throughout the first season of the anime, Horo makes reference to herself as a normal wolf
She is probably trying to be humble or modest or is comparing herself to other wolves in Yoitsu because she isn't a normal wolf compared to others we see on her journey for obvious reasons. As per the wiki you link to,
Holo is a wolf harvest deity that was bound by a promise to the town of Pasloe for several centuries, ensuring a bountiful harvest of wheat for the residents.
I would say she was a deity from the start, or at least had the powers of one (common in Yoitsu?) as she knew that she would keep the promise (but not without caveats such as having bad harvests because of needing the land to recover)
Now, considering that she had come from Yoitsu and we don't have any information on her hitchhiking from Yoitsu like she is on the trip back, as in the anime when we see a flashback from when she first came to Pasloe we don't see her with anyone, I would speculate her binding to wheat is apart of the promise or contract she has made with Pasloe, and possibly how she is able to affect a harvest.
Her still being bound by wheat might mean that the promise is more of a binding contract between her and Pasloe, and it was Holo's decision to leave because she felt she was no longer needed.
Feeling unneeded and that she had kept her promise long enough, she skipped town with a traveling merchant named Lawrence, by 'jumping' from the villagers' wheat to Lawrence's wheat in his wagon.
If her promise is a supernatural binding contract, then she wouldn't necessarily be released from it just because she feels like it.