I think a border of some kind makes a wild area more attractive, partly because it looks purposeful and planned. If you can figure out how to do it, it seems to me you could just let nature overtake the areas you want to stop mowing.
In the beautiful photo posted by @S1969 the border is accomplished simply by the dramatically different heights of the weedy meadow area contrasting against the mowed path. You could also use an attractive fence, a low stone wall, or, more economically, a planted border of some kind to make a boundary between the wild area and your maintained and mowed pasture.
I googled “meadow in landscaping” and clicked on the Images icon to get some ideas. Some look too weedy and just not attractive to me but there are many which I like. But, as seems to happen too often in life, I tend to like the most expensive treatments the best, like the wide hardscape paths which separate the areas, or the beautiful rustic split-rail fences which would probably be a bear to maintain.
Examples from Google Search
For what it’s worth, I think your treed area looks really pretty as is, and I think if you let it go completely it would look great.