So, this is both a realistic description (it’s spring, snow melts, roads get muddy) and a little poem that adjusts our understanding of the story.

Roughly speaking, we understand this description to indicate: “a steadily degrading situation.” The road is “growing worse and worse.” They are driving “into the woods.” There’s “no turning off.” There’s a cost to this trip (those twigs in the face).

This falls on us differently (with more foreboding, say) than a description in which they drove “out of the woods and into the bright sunshine” to find that “the road widened welcomingly” and “low-hanging flowers brushed against her cheeks softly as the cart gently rolled past a joyful peasant wedding.”