Option D: As mentioned in the passage, "...we did not mind the hardness of the road because we had nails in the soles and heels of our boots... with nailed boots it was good walking on the road and invigorating. It was lovely walking in the woods." Option D mentions the same, that there was joy walking in the forest. The word 'lovely' express the joy behind the walking.
Hence option D is correct.
Option A: This line 'path was unaffected by frost' is one of the aspects of the frost, but not the reason.
Option B: This option is not a suitable reason for walking in the pine forest, as mentioned by the line 'we did not mind the hardness of the road because of the nails in the boots'.
Option C: 'The walk was invigorating' on the road, as mentioned here "it was good walking on the road and invigorating. It was lovely walking in the woods."
Hence options A, B and C are wrong.