It is very possible to build one. In fact they are very simple to construct.
Just one example...
A quick search on here shows TONS of threads on hoop coops/runs. I like this design since they end up about 6' tall with straight sides so plenty of head room for both chickens and humans...
Many people use "chicken tractors" to move chickens to fresh pasture. It is totally doable.
The difficulties are largely in moving them around in muddy weather or on uneven ground. The size, design and weight are all factors in moving a tractor.
Predator proofing is also a big consideration...