I had to shovel out an area for them a couple times so they could get to the feed, water, and "chicken shed" which was a small shelter in the run. Definitely extra work with a smaller coop.
Since your run is large and your coop will be for sleeping and laying eggs, you CAN go for a smaller coop. But in my experience, you will have far less flexibility if you have any issues, need to isolate, or want to expand your flock. Also larger coop requires less cleaning. Ventilation is...