Howdy
Yes, the colors are random, because that is how they are formed. It depends on how the chemicals, or water in the case of real bone Case Hardening, swirled around as the colors were being formed. That is the nature of the colors of Case Hardening.
When I bought my Uberti '73 a whole bunch of years ago, I found it used in a local shop. Didn't worry too much about the colors because I got a good deal on it used. This one was built in the 1980s, and I have always felt the colors looked kind of 'blotchy'.
Ten years ago when I decided to buy an Uberti 'Iron Frame' Henry, they were on sale at DIxie Gunworks. I saved $200 buying the iron frame instead of the usual brass frame.
I called up an FFL who was a friend and he ordered the Dixie Uberti Henry for me.
He took a couple of photos of it when he opened the box and sent them to me before I came down to pick it up.
Just like real bone Case Hardening, Uberti case colors will fade over time. They can fade from strong chemicals, finger oils, or even just exposure to sunlight. The colors on my Henry have faded over time, probably mostly from ten years of nothing but Black Powder ammunition.
The colors on this Colt Second Generation from 1973 have faded considerably over the 15 or so years I have been shooting it with Black Powder.
This colors on this First Gen Bisley Colt from 1907 have faded considerably, just from the ravages of time and handling. Notice how the colors are still the most brilliant in the protected areas of the frame in front of the cylinder.
So whatever you finally get, be prepared for the colors to fade over time.