I also second Catherine in this. I watched my sister go through 7 years of a horrible mess with an atheist. I realize Mormons are not atheists, but their faith is VERY different from that of a Christian. As friends it's not a problem. But when you walk with the Lord, and see Him as Your first love, dating someone seriously who has an entirely different view of who He is, and the world in general, it's nearly impossible to be on the same page.
Ultimately scripture tells us it's impossible to serve two masters. Wives are called to submit to our husbands, so that together we serve the same Lord. How can you submit to a husband serving a different god (or idea of God) and still follow the Lord?
It does get tricky when it comes to Mormonism because it so closely resembles Christianity. If you are serious about this person, my recommendation would be to study Mormonism closely, and grill him on his views as well. See just how different it is from your faith, so that you'll know exactly what that relationship will be like down the line.
Though I never dated a Mormon, I have been very close with some (one pursued me at one point). They are great people, I totally understand the desire to get closer! Pray for wisdom, discernment, and be slow to act. I'm 25, so I'm not exactly an older, wiser person ;-) I still hope I can encourage and provide some insight!