just cutting polygons in half
That is not trivial. Even for the quadrilateral case where
The polygon to split may only have four corner points
though that is certainly do-able automatically in SQL. (E.g. see here.)
More vertices will need different approaches.
If geometries vary, you might be best to keep doing it by eye.
In that case there are some friendly tools in Manifold 8.
(1) In the Info pane, enable Show Intrinics (the button second from the right). Write down the area of the original area, from column Area (I).
(2) You can easily bisect any edge. Select the area for editing (Ctrl-Alt-click), then hover over the edge to be bisected, right-click, choose Coordinate > Add Mid-Segment.
I would do that on the longest edge, since that will minimise the length of new fences in the subdivision, if fences are required. (I'm not sure if that is exactly or only roughly right. Just intuition for now, but I hope a good start.)
(3) Now activate snap to areas, and draw a "half" paddock by eye, using the coordinate added in step 2. Disable snaps (spacebar) for that last coordinate, to be adjusted next.
(4) Now also activate snap to segments (and re-enable snaps). Now you can adjust the "half" area drawn in step 3, by shifting coordinates along edges, aiming for an area half that of the original paddock. Inspect Area (I) for the adjusted area after each change.