Wine is an alcoholic beverage and its detection in a urine test depends upon type of test. Alcohol is excreted quickly after absorption through urine and in your case, after 3 hours of its use, no alcohol will be available in the your urine. But one of the metabolites of alcohol is ethyl glucuronide can stay in your system for 80 hours. If you are going to have a EtG test for alcohol then you will be tested positive after 3 hours of use. But not necessarily positive levels harm your results because it can be below your legal limit.
