There are very few tags allotted through the draw here every year one is a public draw that you can apply for and is very hard to draw, although you do get preference points, has it is highly sought after the other is a hunt of a lifetime draw and you can buy unlimited amount of tags for 10 or 20 bucks if I remember right. Only other option is to buy a private lands tag or a governors tag at auction, these go for around $100,000 so for the average joe is unattainable. Only other way to shoot one is to be the guy that owns the land they are living on. One fortunate person and another great reference on Texas bighorn sheep is wtx223 on texasbowhunter.com he has some awesome pics of awesome sheep. User by the name of Shane and 41Chevy both have pics on the site of sheep they shot through the draw as well.
Honestly you best bet for getting a desert big horn would be to save up your pennies or start applying now and hope you are around 20 years from now which is about how long it takes to draw in most states if you ever draw the tag.