The relation for the forest itself seems to be missing. I got here via this untagged way: osm.org/way/321248658 which looks like it is meant to be a big piece of the boundary.

Hi-

If you make sure that paths that connect share a node, software that interprets the data will generally work better.

For example, I expect that this way:

osm.org/way/306192374

Joins up with both Stickney Hill Road and the longer path to the east. Software generally won't make that assumption, it relies on a node being shared by the paths/roads.

I guess data consumers are not widely using it, but it looks like you might also want to make use of the seasonal tag:

osm.wiki/Key:seasonal

That's all,

Max