As Koyasan is nestled in the mountains, the weather can be highly unpredictable. I went up on a clear sunny day in early April. When I reached Koyasan at around 10 am, the thermometer registered 3.5 deg C!! There was fresh fallen overnight snow on the way up on the cable car!
Remember to bring sufficient warm clothing especially if you are planning to stay overnight in one of the shukubos.
For such a peaceful mountain get away, inhabited by monks and spiritual seekers, the cars seem to go really fast down Koyasan's main street. This is, after all, Kansai, a place where Tokyo-ites fear to drive. I recommend taking the bus, and mind your step as you walk along the main road.
The photo is a bit misleading. It shows a broad sidewalk - one of only two in the town. For the most part, it's "share the road."