The supposed White Horse prophecy is not endorsed, supported nor taught by the Church. It really fits more in the rumors and hearsay. It makes for interesting speculation, but it has been discredited. Here is some more documented information about it: http://en.fairmormon.org/Joseph_Smith/Prophecies/White_Horse_prophecy. To be honest I had heard about 3-4 decades ago, but it really is not something that we sincerely consider. 
 
If I may editorialize a bit - many of the things that other churches and people outside the church talk about Mormons is stuff that we rarely teach or talk about. They tend to be things that sound sensational or titillating, but are really not mainstream Mormon teaching. Truth be known we have very definitive courses of study which is where we spend 99% of our time. Church leaders are very prescriptive about what is taught. There is a very set curriculum for everything that is taught. You can see Church manuals here: http://lds.org/manual?lang=eng. For example, we meet every single Sunday in a 3-hour block. There are 3 separate meetings during that block: 
 
1- Sacrament meeting (where the sacrament - bread and water - are passed to the members, hymns sung by congregation and choir, and then about 35 mins of sermons are given by previously assigned members of the congregation - youth, women, and men). When members are asked to give sermons they are given a general topic, asked to use the scriptures (i.e. Bible, Book of Mormon) and not stray beyond the basic teachings of the church. If you go to byu.tv - and look at the schedule for Sunday mornings at 9am MST you can see a Sacrament meeting that is done online for people. 
 
2- Sunday School - We have a 4-year rotation (Old Testament, New Testament, Doctrine & Covenants/Church History, and Book of Mormon) where we have set manuals and lessons for the teachers and students. Teachers are asked to teach from the manual and scriptures and not deviate. 
 
3- Separate classes for Men, Women, Youth, and children. Here again - there are set lessons. 
 
 
Additional training from our leaders comes from local and church-wide leaders. The church-wide leadership teaching and training is mainly done in what we call General Conference. This is done in 10 hours of broadcast meetings over a weekend. You can see/hear/read the latest addresses here: http://lds.org/general-conference?lang=eng. These teachings/talks are all very basic teachings about the fundamental teachings of the church. 
 
The Church is very focused about teaching what is really the doctrine of the Church and not straying. That is why we don't really talk about the fringe/rumor/scuttlebutt of the church. 
 
A good manual about the basic teachings of the church (which is one of the Sunday School classes taught on Sunday) can be found here:https://lds.org/manual/gospel-principles?lang=eng 
 
So as you can see - the Church does not stray from teaching basic principles and actually discourages speculative subjects/topics. So when you ask about the White Horse Prophecy - it's not something that is believed or taught by the Church. 
 
Hope that helps. 
 
Thanks

There is no White Horse Prophecy in the LDS Church as Jett was talking about. There is speculation mostly from Anti-Mormons because a friend of a friend stated that the Prophet said something shortly before going to Carthage Jail where he was martyred for his beliefs.  
 
Now that is something to preach on, how so called Christian men murdered two men in cold blood because of there faith in Christ. If any sermon needs to taught about the LDS faith it is how Christlike the pioneers of our Church deduced the wicked and satanic acts against them from there fellow Christians.  
 
There is no 'Mormon Royalty" almost every members who can trace his roots back to the handcart companies that were forced on an exodus across the nation is this so called "royalty". With the small number of pioneers that started out many of the families are connected to each other through marriage.  
 
Only converts like me cannot claim to be somehow related to one of the major families of the LDS pioneers. These families have no preference in Church callings or in privilege. They have to be just a worthy and every other member to partake the sacrament or attend the temple.  
 
The problem is though is that too many rather find a good story than look at the reality of things. Thousands of "prophecies" like White Horse arose AFTER the death of the Prophet. Half of the LDS folklore comes from alleged things the prophet said in his last days but never wrote down or told anyone else, except this one person who told another person.  
 
It is easy to claim a dead man said something, since he can not confirm or deny anything anymore.