2 Answers

                   Polled Angus Cow

Understand what polled cattle are. Polled cattle have absolutely no horns, nor scurs nor bare spaces where a pair of horns may have been, whatsoever. The best way to tell is if a cow, bull, steer or heifer is polled is by looking at the poll, itself located just above and between the ears. If it forms some sort of peak, then the animal is indeed polled, not horned, scurred or dehorned.

 http://www.wikihow.com/Identify-Horned,-Scurred-and-Polled-Cattle

Yes, they are "genetically hornless".  For example there are Herefords and Polled Herefords.  The Herefords are like most cattle, born with the ability to grow horns.  (Luckily for mom, not "born with horns"!)  The reason that you do not see more horns on most cattle is that they have been removed by various techniques.  The cowboys would use dehorners, iron scoops on a long rod, which have been heated in fires.  These would burn the "horn bud" off.  Think of this as a bud on a plant, if it is broken off, you do not get the branch, flower, or fruit (depending upon which type it was).  Most cattle are dehorned using electric dehorners today.  Also they can use a chemical paste to burn them off.  If not done, and they begin to grow, they can be sawed off, a much more stressful, and bloody job.  It is done for safety to both the farmers and the cattle.  In commercial production today, animals are in closer quarters, and they can hurt themselves and each other with their horns.  If done at a young age, the dehorning is relatively painless...  The good outweighs the pain.