Book of Hosea Chapter 1 Vs. 7

 Hosea's Wife and Children

But I will have mercy upon the house of Judah, and will save them by the LORD their God, and will not save them by bow, nor by sword, nor by battle, by horses, nor by horsemen. Hos. 1:7

I will have... God chose to intervene on behalf of Hezekiah when Jerusalem was besieged at the hands of the Assyrians (in 701 B.C.; 2Kgs. Chapter 19; Isa. Chapter 37).

This is just saying that Judah will not be overrun by Assyria.

and will save...They will be spared from this, because they have not been as unfaithful to God as Israel (10 tribes), has been. They would be taken captive, but not by Assyria, and not until over 100 years later. They had a few godly leaders, and Israel did not. They will not be saved in battle; they will be saved from battle.

and will not... Judah will not have to depend on weapons to save them. God will save them. Perhaps this refers to the battle where Sennacherib, king of Assyria, lost 185,000 men in one night (2Kgs. 19:35). The angel of the Lord killed them. God won the battle for Judah. This was during the reign of Hezekiah. This is the very same army that had overrun Israel (10 tribes), and defeated them.

The light of God’s grace shines through the gloom of impending judgment. Judah, the Southern Kingdom, in contrast with Israel, would experience the Lord’s love in the form of deliverance from the Assyrians. This would not be accomplished through human military might (symbolized by the bow, sword, etc.), but by the Lord’s intervention. This promise was fulfilled in 701 b.c. when God supernaturally annihilated 185,000 soldiers in the powerful Assyrian army in one night thereby ending its campaign against Judah (2Kgs. 19:32-36).

The light of God’s grace shines through the gloom of impending judgment. Judah, the Southern Kingdom, in contrast with Israel, would experience the Lord’s love in the form of deliverance from the Assyrians. This would not be accomplished through human military might (symbolized by the bow, sword, etc.), but by the Lord’s intervention. This promise was fulfilled in 701 b.c. when God supernaturally annihilated 185,000 soldiers in the powerful Assyrian army in one night thereby ending its campaign against Judah (2Kgs. 19:32-36).