It depends on the school and their policies. That being said, you did not specify whether you were just arrested or convicted. If you have not been convicted contact a dwi attorney to see if you in fact will be found guilty. A follow up question you may have is whether you will be allowed to sit for the bar exam. Most States have a moral fitness portion on the background check and a substance abuse related offense does raise questions. You should contact the local bar and determine how it will affect your chances and go ahead and address the issue of whether or not you have a problem. Many States have a Legal Assistance Program in place and offer counseling and treatment options if it is determined you have a problem. The State Bars also rely heavily on the recommendations of the program administrators to determine if you will be a risk to future clients. From a practical standpoint one should not hurt you too bad; two could destroy your future plans.
School policies vary. Get a copy of the schools code of conduct. You will probably be allowed to continue. If convicted you can expect to have to meet with the character and fitness committee to answer questions about this before being admitted to the bar.