I've trailered a 20' center console into Winter Harbour 3 times over the past 4 years, last time was in July. It's perfectly fine. Go slow and you won't have any problems at all. I've never had any issues, no flat tires etc. The road is well marked, just pay attention at the intersections and follow the signs. There are some sections closer to Winter Harbour with moderate potholes. I've never seen much sharp rock on the road to cause concern about tires.
Watch out for logging traffic. I have had to back up to a pull out to let a truck pass.
Edit: Just noticed you are looking at the road from Coal Harbour, I can't comment on that route. I've only taken the Holberg Rd.