The rhyme scheme seems intended to suggest very subtly the look and feel of falling snow. For example, the first stanza's rhymes are AABA. Then the B is caught up in the second stanza and becomes the dominant rhyme in BBCB. And in the third line the C becomes dominant in CCDC. The only exception to this scheme is in the final stanza which rhymes DDDD, whereas we might expect it to be DDED.
Why doesn't Frost rhyme AAAB, then BBBC, and CCCD, if he wants to suggest falling snowflakes? It would appear that he wants to "catch" the B and then "catch" the C, and so on, before it falls completely. If A can be visualized as a falling snowflake, then B would be a snowflake falling behind it--and so forth. Then when he gets to D in "sweep" in the third stanza, he repeats the D rhyme throughout the entire last stanza and even repeats the entire line: "And miles to go before I sleep, / And miles to go before I sleep," in order to give the impression of finality. The falling snow has, in effect, piled up on the ground, and he is leaving the beautiful scene behind him. In other words, the DDDD represents, not falling snow, but fallen snow.
This is a lot to read into Frost's rhyme scheme, but it may help to explain the strong effect of this apparently simple short poem. We feel as if, with Frost, we have taken a few minutes out of our own lives to watch, and also to feel, the beautiful winter snow scene which everyone else in the world, including the man who owns the woods, is missing.