Scripting would be more elegant, of course, but then there's always a brute force approach with point and click editing that might be quicker.
1. The arrangement of grid lines is supposed to be parallel to some side of the paddock. OK. Pick that side and in a new layer draw a line that uses snap to duplicate that desired side (a straight line segment).
2. Calculate the spacing you want between lines in that direction.
3. Copy the line you just drew, and then shift the drawn line the desired spacing direction one step.
4. Paste the copied line. You now have two parallel lines, one desired interval apart. Copy those.
5. Shift the two lines twice the interval. Paste. You now have four parallel lines the desired interval apart.
6. Repeat that until you have enough parallel lines that extend all the way across the paddock.
7. Using copy and shift, make copies that extend those lines in the direction of the lines up and down so you have what appear to be longer parallel lines that completely cover the paddock in the direction of the lines.
8. Copy all those, rotate the lines 90 degrees, and then paste the lines previously copied. You now have a big checkerboard of lines perpendicular to each other that completely cover the paddock.
9. Make enclosed areas from that checkerboard.
10. Use the original paddock to clip those enclosed areas. You now have a checkerboard of square areas that align to the desired side of the paddock and which have been clipped to be inside the paddock.
The above is a thought experiment, not something I've tried in real life. But I've done similar things and it goes remarkably quickly, probably faster for a one-off than writing and debugging a script. :-)