I have three good size Golden Euonymus shrubs that I would like to cut back. It's my understanding that I should leave at least a third of the shrub. They are all a good size and it would be a pretty big project, however, I'd like to get some good advice on the matter.

Euonymus is very tough stuff in my experience. More problem is all that green is not going back to golden.
Wait for more advice. If you cut way back all the green you will have a very weird shrub for a while.

I have three Golden Euonymus on my property two of which are quite green however the third one I've pampered for practically thirty years or more and the others which get a good deal of sun is more on the green side.
Thank you for your thoughts on the matter,

That one looks all gold and nice

Still waiting for comments from those who know more - maybe they are out working with their own shrubs.
I had a different species ('Manhattan') and would hack them back any old way to keep them down to size. They always grew back. I cut a hedge 5 foot tall and 7 foot wide down to stumps and they regrew.

Cutting this late in fall, I predict would leave either bare stems ends or tender shoots. Not great.

Personally... I'd consider propagating the shrub that actually is the desired colour.

Those euonymus shrubs that have reverted to green should be removed.

These things are very easy to propagate...

Throw away the hedge shears... in the Early Spring... cut back some limbs and shove down into a nice seed bed... keep watered... they root pretty fast... Or... just layer some limbs...

In the future... avoid the compulsion to carve them into balls...

stone said:

In the future... avoid the compulsion to carve them into balls...

But that look may be a personal preference, many like a more formal look to their gardens.