What does the poet mean by saying, "stands about the woodland ride"?
This is old-fashioned language for a cherry tree standing by the side of a road which leads into or through the woods.
"Stands about" means standing on either side of, or next to.
The image this should create in your mind is that of a road or path through the woods which, at some point, is lined with cherry trees. Perhaps the other, taller trees behind the cherries have not yet begun to bloom or put out any leaves, but the cherry trees have already burst into white flower. They would stand out and be easy to spot.
Although the poem speaks of "the cherry," as if there is only one, the implication is that there are many. The poet is planning to look at all the cherry trees out there. This is similar to how we might say, "The bear hibernates through the winter," meaning all bears. In the last line of the poem,
About the woodlands I will go/To see the cherry hung with snow
it is clear that the poet is planning to take a long ramble all over the woods to enjoy the many cherry trees that he knows are there.