An 'old-timer' once said to me that every good dark red Shorthorn had a white in the last three generations.
I'd like to add that, in my herd at least, all good Shorthorns have horned genetics in the last three generations as well. We made the decision to not keep any horned male progeny about three years ago, but quickly rescinded our decision. We sent one away, as a polled, for performance testing and he came back with horns! See the attached picture, the other bull is an older Saskvalley Yesterday 116Y son.
We couldn't sell him, to save face after publishing our decision not to sell horned bulls, he was arguably the best bull in his contemporary group, so used him in our crossbred cattle, brought him back for use in our registered herd for two mating periods, different properties, sent him back to the crossbred herd, where he is now, and will probably use him in our satellite registered herd in a year or two as well.
The bottom line is, don't make arbitrary decisions and don't discount white and horned Shorthorn bulls!