As I'll be leading a hike at the end of the month that crosses High Bridge, I wanted to stop by to see if much of the park was still blocked off by construction. It turns out the answer is it's not - only the area immediately around the water tower is off-limits.
I opted to take sidewalks alongside Morningside, St. Nicholas, and Jackie Robinson Parks, since they were shoveled and pretty reliably clear from snow earlier in the week. I did the same for Highbridge Park, as I wanted to get a good view of the construction or lack thereof.
At High Bridge, I crossed over and briefly stood in the Bronx before heading back. There I took a well-cleared bike path, but otherwise I retraced my steps home.