Adam Clarke on Hosea 1:7

But I will have mercy upon the house of Judah - I will spare them as a kingdom after Israel has been carried away into captivity by the Assyrians.

And will save them by the Lord their God - Remarkably fulfilled in the supernatural defeat of the army of the Assyrians, see 2Kgs 19:35; and so they were saved not by bow, nor by sword, nor by battle, nor by horses, nor by horsemen. The former expression may mean, not in war by horses, i.e., yoked to war chariots, nor by horsemen - nor by cavalry, however efficient such troops might have then been deemed.