My process is a bit hard to explain. I don't sketch anything, just work straight into the computer and have a bad habit of deleting progress work so there's no real visual story I can show.
I pretty much exclusively use pen tool, shapes, align and pathfinder.
Those icons are part of a larger branding job so I first worked on the logo, colour palette and overall concept.
The colour palette was originally even more dusty/muted to reflect the Australian landscape but the client wanted some brighter colours so its a bit of a compromise.
The concept I came up with was this idea of 'pathways' crossing over and under each other with different colours to represent the stages cattle go through (on their way to your plate).
I started with the animals, got a bunch of reference images of cattle and then started blocking out shapes to get the proportions roughly correct. I pretty much just use rectangles and circles when I start drawing. Rectangles are turned 45º if I need an angle. Then I round corners and adjust shapes until it looks right.
Once that was done I deleted parts of the shapes and joined them up to other shapes. Important to have shapes align so they can connect cleanly. Lot's of trial and error and tweaking.
Some of the other icons were easy. Just your standard ones seen a million times before drawn in the style developed for this job.