What does Wordsworth mean by "the winds that will be howling at all hours"?

Wordsworth is talking about how the wind sounds: he says it howls. While the words are self-explanatory, the context needs to be explained.
Wordsworth is saying in this sonnet that modern humans are out of "tune" with nature. We feel alienated from the natural world. That is because we spend too much time apart from it, focused on earning and spending money.
For Wordsworth, who found God's spirit, redemption, and a deep peace and joy in the natural world, this is a serious problem, one he laments in this sonnet.
The poem implicitly compares the unimaginative way we hear the wind in the modern world to how the ancient Greeks heard it: to us, it merely howls. The Greeks, however, understood nature as a spiritual force. To them, the sound of the howling wind was filled with poetry and tied to the music of the gods. It wasn't merely some annoying outside force howling but Triton, the messenger god of the sea, blowing his horn. Wordsworth would rather embrace nature in the same imaginative and spiritual way as the Greeks did than in the dull terms of his own time.

Wordsworth was incredibly enraptured with the beauty and magic of nature and increasingly frustrated with the average human's preoccupation with the fast-paced, modern, consumerist world. He uses this line, describing winds that should ordinarily be impossible to ignore, as an example of a storm that is so majestic that it should be able to get anyone's attention. However, the speaker, and everyone else living in the world, cannot appreciate the beauty. The noise and interference of modern life has left them "out of tune." In fact, at the end of the poem, Wordsworth states that he would have rather been born in some pagan society. This way, at least he could appreciate the primal beauty of nature in its wholeness rather than being constantly tugged away from it by the material world.

This line is particularly effective because of the assonance of the "ow" sounds in "howling" and "hours." It's also powerful because of the contrast between the calm winds at present—"up-gathered like sleeping flowers"—and their usual howling. The speaker of this poem feels besieged and unable to appreciate the beauty and power of nature because the modern world has left him "out of tune." It's interesting to consider Wordsworth's own situation at the time of the poem's publication. Wordsworth was under great financial pressure: he had only recently married, and his wife had given birth to three children. His sister Dorothy also lived with them in their small cottage. Wordsworth was the sole breadwinner, and he composed much of his poetry outside the house while walking in nature. We might speculate that some of the speaker's distress here is Wordsworth's own: an appreciation for natural beauty and the poetry of nature wars with practical realities and the cares of the modern world that are always "too much with us." His struggle is one many can still relate to; to many of us, Wordsworth and his wife and sister could lead a simple life compared with the way many people live today with their automobiles, television, computers, medical insurance, and all the other things they either need or want. When the speaker of the poem says he would rather be a pagan, he is perhaps thinking that he would like to have a really simple life—one without financial pressures and complexities. If his financial situation was critical, the situation of millions of young couples raising children today is chaotic. A lot of busy people must be thinking that they would rather give up all their possessions just to have peace of mind and to be able to call their souls their own.