Planters would be the way to go- especially if you have restrictions in regards to fencing. I've linked a simple large scale planter below which is available in a wide array of color options. You could plant hedges or tall grasses to fully obscure the pump!

https://www.urbilis.com/dividum-planter/

Urbilis:

On the page you linked to, the color selection drop-down menu isn’t working for me.

The first thing I would do is take a good look at the rules pertaining to fences and screening myself and make sure I understand them. Possibly you are in a grey area as while what you would use to cover a utility might appear as a "piece" of fence, it would NOT be a fence proper, or qualify legally as a "fence." Depending on how the rules are written, you may have a great case that warrants you to screen the pool equipment with something that is built out of fence-like materials ... especially, if it would permit you to use wrought iron instead of wood. I know from first-hand experience that the people who manage neighborhood rules and regulations sometimes just do not know how to read them. Sometimes, these people are volunteers performing civic duty and sometimes sometimes they're professionals. In either case they can make errors of judgement that go on for years (because that's how a predecessor interpreted a rule.)

In my estimation, covering the equipment warrants a physical panel of some sort. Using plants, which are big and bushy, simply complicate the matter.